{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<img src=\"http://hilpisch.com/tpq_logo.png\" alt=\"The Python Quants\" width=\"35%\" align=\"right\" border=\"0\"><br>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Python for Finance"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Analyze Big Financial Data**\n",
    "\n",
    "O'Reilly (2014)\n",
    "\n",
    "Yves Hilpisch"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<img style=\"border:0px solid grey;\" src=\"http://hilpisch.com/python_for_finance.png\" alt=\"Python for Finance\" width=\"30%\" align=\"left\" border=\"0\">"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Buy the book ** |\n",
    "<a href='http://shop.oreilly.com/product/0636920032441.do' target='_blank'>O'Reilly</a> |\n",
    "<a href='http://www.amazon.com/Yves-Hilpisch/e/B00JCYHHJM' target='_blank'>Amazon</a>\n",
    "\n",
    "**All book codes & IPYNBs** |\n",
    "<a href=\"http://oreilly.quant-platform.com\">http://oreilly.quant-platform.com</a>\n",
    "\n",
    "**The Python Quants GmbH** | <a href='http://pythonquants.com' target='_blank'>www.pythonquants.com</a>\n",
    "\n",
    "**Contact us** | <a href='mailto:analytics@pythonquants.com'>analytics@pythonquants.com</a>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Stochastics"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Random Numbers"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false,
    "uuid": "fba5b184-6652-4665-9053-1741d9b16bb9"
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import numpy.random as npr\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false,
    "uuid": "8763b99e-6b02-4003-8567-c0f505986e5a"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 0.38149781,  0.67472245,  0.52930643,  0.82789491,  0.32402136,\n",
       "        0.91759317,  0.70999488,  0.91402186,  0.38792711,  0.14082676])"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "npr.rand(10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false,
    "uuid": "16f2a7c4-62dd-4d0f-bde9-fafb61e0fb64"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0.54056252,  0.34555326,  0.89572902,  0.26026525,  0.43574886],\n",
       "       [ 0.60084973,  0.20991542,  0.86092347,  0.26358636,  0.89639337],\n",
       "       [ 0.1549069 ,  0.45802605,  0.91081355,  0.08183648,  0.94818369],\n",
       "       [ 0.64659773,  0.44279118,  0.24208235,  0.91540828,  0.92345946],\n",
       "       [ 0.70147286,  0.14103389,  0.87856977,  0.57875223,  0.17051678]])"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "npr.rand(5, 5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false,
    "uuid": "2d14b433-a7da-4aac-a534-56ab4c8a5d84"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 6.91294755,  6.17425098,  7.04935596,  7.58279497,  8.91989095,\n",
       "        6.53815176,  8.52897859,  7.66654959,  8.37488787,  7.26440555])"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a = 5.\n",
    "b = 10.\n",
    "npr.rand(10) * (b - a) + a"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false,
    "uuid": "a05adb2b-5704-4189-b0e8-19318ac3f0b9"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 6.16321316,  9.32303829,  9.97670443,  8.60697599,  7.71428921],\n",
       "       [ 7.50955004,  5.74440407,  5.83774446,  7.50908669,  8.96393653],\n",
       "       [ 8.80295133,  6.53463824,  8.77144642,  5.92119901,  6.40813   ],\n",
       "       [ 6.10818935,  8.39621717,  7.15254198,  9.1797606 ,  7.80898567],\n",
       "       [ 8.9060506 ,  9.08388979,  9.78395034,  7.7338426 ,  8.73691598]])"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "npr.rand(5, 5) * (b - a) + a"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false,
    "uuid": "4618b170-6bd3-4500-905a-0fe402f198c1"
   },
   "outputs": [],
   "source": [
    "sample_size = 500\n",
    "rn1 = npr.rand(sample_size, 3)\n",
    "rn2 = npr.randint(0, 10, sample_size)\n",
    "rn3 = npr.sample(size=sample_size)\n",
    "a = [0, 25, 50, 75, 100]\n",
    "rn4 = npr.choice(a, size=sample_size)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false,
    "uuid": "d03c9514-c224-4d2b-ad2a-9285058823b0"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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sSgxpuhuaK9lLVbruyi3m0hxV6piD0dMcnDEHZRAEw2IspxaTlOs1KniKU1XlJe/n5Kls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\nMi3Bn7j7u3vfTMeFAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fd5e9dd2510>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ((ax1, ax2), (ax3, ax4)) = plt.subplots(nrows=2, ncols=2,\n",
    "                                             figsize=(7, 7))\n",
    "ax1.hist(rn1, bins=25, stacked=True)\n",
    "ax1.set_title('rand')\n",
    "ax1.set_ylabel('frequency')\n",
    "ax1.grid(True)\n",
    "ax2.hist(rn2, bins=25)\n",
    "ax2.set_title('randint')\n",
    "ax2.grid(True)\n",
    "ax3.hist(rn3, bins=25)\n",
    "ax3.set_title('sample')\n",
    "ax3.set_ylabel('frequency')\n",
    "ax3.grid(True)\n",
    "ax4.hist(rn4, bins=25)\n",
    "ax4.set_title('choice')\n",
    "ax4.grid(True)\n",
    "# tag: rand_samples\n",
    "# title: Simple pseudo-random numbers\n",
    "# size: 70"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false,
    "uuid": "fb2966ea-91ff-49c7-80e6-24bd6162cc5a"
   },
   "outputs": [],
   "source": [
    "sample_size = 500\n",
    "rn1 = npr.standard_normal(sample_size)\n",
    "rn2 = npr.normal(100, 20, sample_size)\n",
    "rn3 = npr.chisquare(df=0.5, size=sample_size)\n",
    "rn4 = npr.poisson(lam=1.0, size=sample_size)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false,
    "uuid": "3f790711-f965-4a10-b3df-47cc85d708d3"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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LrQyNqQOV0AjngvWMuWGNsHrkoRFK+g/gRGBH4D0R8TJJd0TETulxAbe39juudZnCGmGd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\nJEkmTTbCJEmSZNL8A8vSP6USA8O2AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fd5e9dd2350>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ((ax1, ax2), (ax3, ax4)) = plt.subplots(nrows=2, ncols=2, figsize=(7, 7))\n",
    "ax1.hist(rn1, bins=25)\n",
    "ax1.set_title('standard normal')\n",
    "ax1.set_ylabel('frequency')\n",
    "ax1.grid(True)\n",
    "ax2.hist(rn2, bins=25)\n",
    "ax2.set_title('normal(100, 20)')\n",
    "ax2.grid(True)\n",
    "ax3.hist(rn3, bins=25)\n",
    "ax3.set_title('chi square')\n",
    "ax3.set_ylabel('frequency')\n",
    "ax3.grid(True)\n",
    "ax4.hist(rn4, bins=25)\n",
    "ax4.set_title('Poisson')\n",
    "ax4.grid(True)\n",
    "# tag: rand_distris\n",
    "# title: Pseudo-random numbers from different distributions\n",
    "# size: 70"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Simulation"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Random Variables"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false,
    "uuid": "ac34499c-4675-457e-a0ac-40b8efcdb72e"
   },
   "outputs": [],
   "source": [
    "S0 = 100  # initial value\n",
    "r = 0.05  # constant short rate\n",
    "sigma = 0.25  # constant volatility\n",
    "T = 2.0  # in years\n",
    "I = 10000  # number of random draws\n",
    "ST1 = S0 * np.exp((r - 0.5 * sigma ** 2) * T \n",
    "             + sigma * np.sqrt(T) * npr.standard_normal(I))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false,
    "uuid": "7fc0b66a-9ce3-4c5e-bb99-d5e0363a6678"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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AbWQH+LjyvpOR4px3ipkgzVwpZuqXBwszM+vKNYvOxyHdOfPRnedf7vvo5WfT\npxexYXLNwiwhvQ8Avq6GjYbkpqEkbZY0K+keSe+oOs9oy6oO0EZWdYA2sgHuazDnl0pxzjvFTJBm\nrhQz9SupwULSwcD/ADYDG4CzJT2z2lSjbKbqAG04UzeSOPnkk5P7QujMTFr9tCDFXClm6ldSgwX1\n62/fGxFzEfEw8LfAaWUd7HOf+xxPfOIRHHroY2+HHXZEWYccsoe6Nxm6lZmpt7MBBHARRd6dDPNM\nAw89lOJzl2auFDP1K7XB4mjg2w3r+/Jtpdi/fz8HHzzBz3/+j4+5wavLOqStWP1PT3UeFFr3uzxO\nV2MpSa3APfSPgfziF3fypCf90WO2/fKXy+Ut5FzVAdqYqzpAG3NVB2hjrs22Xk4/075tvwPGu971\nruQ+rTU3N1d1hBYpZupXUh+dlfRC4OKI2JyvbwUeiYjLGtqkE9jMbIT089HZ1AaLQ4BvAL8LfBfY\nDZwdEXdVGszMbIVLahoqIvZLejNwI3Aw8EEPFGZm1UvqnYWZmaUptU9DLSmVL+xJmpN0u6Q9knbn\n21ZL2inpbkk7JI2VnOEqSfOS7mjY1jGDpK15v81K2jTETBdL2pf31R5JrxpypmMl7ZL0dUl3Srog\n315ZXy2Rqeq+erykWyXNSNor6a/y7VX2VadMlfZVfpyD82N/Ol+v9PevQ6bB9VNEjMSN+rTUvcA4\n8Djq36R6ZkVZ7gNWN217D/Cf8uV3AJeWnOGlwInAHd0yUP+C40zeb+N5Px40pEwXAW9t03ZYmdYC\nE/nyE6nXxJ5ZZV8tkanSvsqPdWj+7yHALcBLEvi5apcphb56K3A1cH2+Xmk/dcg0sH4apXcWQ/3C\nXgHNnyo4FdiWL28DTi/z4BHxD8APC2Y4DbgmIh6OiDnqPxgbh5QJ2n++c1iZ7o+ImXz5J8Bd1L+7\nU1lfLZEJKuyrPM/P8sVV1P9A+yHV/1y1ywQV9pWkY6h/IevKhhyV9lOHTGJA/TRKg8VQv7DXRQA3\nSbpN0hvzbWsiYj5fngfWVJCrU4ajqPfXgmH33Z9I+pqkDza8NR96Jknj1N/53EoifdWQ6ZZ8U6V9\nJekgSTPU+2RXRHydivuqQyaotq/eC7wdeKRhW9U/U+0yBQPqp1EaLFKqxL84Ik4EXgW8SdJLG++M\n+vu8SvMWyDCsfP8TWAdMAN8D/nqJtqVlkvRE4JPAWyLix485aEV9lWf6RJ7pJyTQVxHxSERMAMcA\nvyPp5Kb91WUjAAAEE0lEQVT7h95XbTLVqLCvJL0GeCAi9tDhW5HD7qclMg2sn0ZpsPgOcGzD+rE8\ndmQcmoj4Xv7v94Frqb99m5e0FkDSkcADFUTrlKG5747Jt5UuIh6IHPW3xwtvdYeWSdLjqA8UH4mI\n6/LNlfZVQ6aPLmRKoa8WRMSPgM8AzyORn6uGTM+vuK9eBJwq6T7gGuDlkj5Ctf3ULtOHB9lPozRY\n3AYcL2lc0irgTOD6YYeQdKikw/Plw4BNwB15li15sy3Ade33UKpOGa4HzpK0StI64HjqX3gsXf5L\ns+D3qPfV0DJJEvBBYG9EXN5wV2V91SlTAn311IVpCklPAF4B7KHavmqbaeFFOTfUvoqId0bEsRGx\nDjgL+FxE/CEV9lOHTH800J+pfqvvw7xRn/b5BvVizNaKMqyj/imCGeDOhRzAauAm4G5gBzBWco5r\nqH/L/ZfUazlvWCoD8M6832aBVw4p0znAh4Hbga9R/+VZM+RML6E+hztD/YVvD/VT4FfWVx0yvSqB\nvno28NU81+3A27v9bA+hrzplqrSvGo71MhY/eVTp71/DsWoNmT4yqH7yl/LMzKyrUZqGMjOziniw\nMDOzrjxYmJlZVx4szMysKw8WZmbWlQcLMzPryoOFrQiSvtRj+9rCaZ77PO6kpPf3u5+y92nWjQcL\nWxEi4sVVHXpE9mm2JA8WtiJI+kn+b01SJunvJN0l6aMNbTbn275C/dQIC9sPU/3CTrdK+qqkU/Pt\nl0v683z5lZI+3yXDv5D0CUm789uL8jOq3ifpyQ3t7snbtrQfcLeYFZbUNbjNStT41/gE9Yu/fA/4\nUv4i/FXgA8DJEfFNSR9veMyfAjdHxDn5eYpulbQT2Ap8WdIXgfdRP2XHUt4HvDciviTpacANEbFB\n0qeoD07Tkk4C7ouI70v6WHP7PHfbM52alcmDha1EuyPiuwD5dRLWAT+j/iL9zbzNR4F/ly9vAl4r\n6W35+q8BT4uIb6h+PZN/oH6a8fu6HPcU4Jn18wgCcLikQ4GPA38BTFM/CdzHl2h/2AH8f8365sHC\nVqJfNCz/ivrvQXMdoPmv99dFxD1t9vUc4PsUu5iNgJMi4peP2SjdAhwn6anUr2D27i7tXbOwoXPN\nwqw+UMwC45KekW87u+H+G4ELFlYknZj/+3Tq1zw+EXiVpHaXpWwcdHY07WcCHr1QzrXUr3S2NyJ+\nuFR7PA1lFfBgYStFdFiub4j4BfVpp8/kBe75hnZ/CTxO0u2S7gTelW+/EviPEXE/cC5wZX6tlebj\nLuznAuD5ql/i8ussTnNBferpD1icglqqfeVXYrSVx6coNzOzrvzOwszMuvJgYWZmXXmwMDOzrjxY\nmJlZVx4szMysKw8WZmbWlQcLMzPryoOFmZl19f8BUEv7HxBUDb8AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fd5e9e4b610>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.hist(ST1, bins=50)\n",
    "plt.xlabel('index level')\n",
    "plt.ylabel('frequency')\n",
    "plt.grid(True)\n",
    "# tag: gbm_T_sn\n",
    "# title: Simulated geometric Brownian motion (via +standard_normal+)\n",
    "# size: 60"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false,
    "uuid": "c37a0783-81b1-449f-924e-f792ba5017aa"
   },
   "outputs": [],
   "source": [
    "ST2 = S0 * npr.lognormal((r - 0.5 * sigma ** 2) * T,\n",
    "                        sigma * np.sqrt(T), size=I)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false,
    "uuid": "fea07d0c-7fc1-4ab8-8b21-fc36e73c3151"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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g/ZnTJ4snTtiLiEPAzAl7qWj/lsFKYFO5vAm4ZrhxICK+AHyvbXO3XFcDmyPi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\nwcLMzHryYGFmZj15sDAzs57+P4gAqG+4zeb/AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fd5e9ba0710>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.hist(ST2, bins=50)\n",
    "plt.xlabel('index level')\n",
    "plt.ylabel('frequency')\n",
    "plt.grid(True)\n",
    "# tag: gbm_T_ln\n",
    "# title: Simulated geometric Brownian motion (via +lognormal+)\n",
    "# size: 60"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": false,
    "uuid": "e5e17dcf-21f4-42ee-bcec-21103aaa8bb3"
   },
   "outputs": [],
   "source": [
    "import scipy.stats as scs"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": false,
    "uuid": "d6f800c9-f38f-4fe1-8cb5-fe9253f1194c"
   },
   "outputs": [],
   "source": [
    "def print_statistics(a1, a2):\n",
    "    ''' Prints selected statistics.\n",
    "    \n",
    "    Parameters\n",
    "    ==========\n",
    "    a1, a2 : ndarray objects\n",
    "        results object from simulation\n",
    "    '''\n",
    "    sta1 = scs.describe(a1)\n",
    "    sta2 = scs.describe(a2)\n",
    "    print \"%14s %14s %14s\" % \\\n",
    "        ('statistic', 'data set 1', 'data set 2')\n",
    "    print 45 * \"-\"\n",
    "    print \"%14s %14.3f %14.3f\" % ('size', sta1[0], sta2[0])\n",
    "    print \"%14s %14.3f %14.3f\" % ('min', sta1[1][0], sta2[1][0])\n",
    "    print \"%14s %14.3f %14.3f\" % ('max', sta1[1][1], sta2[1][1])\n",
    "    print \"%14s %14.3f %14.3f\" % ('mean', sta1[2], sta2[2])\n",
    "    print \"%14s %14.3f %14.3f\" % ('std', np.sqrt(sta1[3]), np.sqrt(sta2[3]))\n",
    "    print \"%14s %14.3f %14.3f\" % ('skew', sta1[4], sta2[4])\n",
    "    print \"%14s %14.3f %14.3f\" % ('kurtosis', sta1[5], sta2[5])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": false,
    "uuid": "980679e8-56af-49e3-85f3-4b4d1ed90312"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "     statistic     data set 1     data set 2\n",
      "---------------------------------------------\n",
      "          size      10000.000      10000.000\n",
      "           min         27.002         25.828\n",
      "           max        407.204        362.143\n",
      "          mean        109.731        110.383\n",
      "           std         39.714         39.655\n",
      "          skew          1.070          1.040\n",
      "      kurtosis          1.897          1.771\n"
     ]
    }
   ],
   "source": [
    "print_statistics(ST1, ST2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Stochastic Processes"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Geometric Brownian Motion"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": false,
    "uuid": "a6b64214-0041-49cb-b7a8-7b4965d1d03a"
   },
   "outputs": [],
   "source": [
    "I = 10000\n",
    "M = 50\n",
    "dt = T / M\n",
    "S = np.zeros((M + 1, I))\n",
    "S[0] = S0\n",
    "for t in range(1, M + 1):\n",
    "    S[t] = S[t - 1] * np.exp((r - 0.5 * sigma ** 2) * dt \n",
    "            + sigma * np.sqrt(dt) * npr.standard_normal(I))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": false,
    "uuid": "969180df-b1f3-4f6d-8ec6-21cadbec06f1"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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1i87Hof6595Tm6es+XsrZOu9j2H6/bOVyzcJsyCz147cecCwFyU1DSTpJ0oyk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\nP3LSwN/W4w16AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fd5e1488090>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.hist(S[-1], bins=50)\n",
    "plt.xlabel('index level')\n",
    "plt.ylabel('frequency')\n",
    "plt.grid(True)\n",
    "# tag: gbm_dt_hist\n",
    "# title: Simulated geometric Brownian motion at maturity\n",
    "# size: 60"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "collapsed": false,
    "uuid": "37d83fc1-6b2d-4d94-a5d1-75d2ba569283"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "     statistic     data set 1     data set 2\n",
      "---------------------------------------------\n",
      "          size      10000.000      10000.000\n",
      "           min         27.244         25.828\n",
      "           max        402.432        362.143\n",
      "          mean        110.672        110.383\n",
      "           std         40.514         39.655\n",
      "          skew          1.109          1.040\n",
      "      kurtosis          2.058          1.771\n"
     ]
    }
   ],
   "source": [
    "print_statistics(S[-1], ST2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "collapsed": false,
    "uuid": "c424f261-aa3f-4b04-9b5d-bb6824107fa0"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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nE6rKb8aNk9W+DWJj36WqKkxNPVC+hIMnDl045GFzyaxpZOvWZM2aoj4KCiL/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\nuNCaS+TkS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PMVBeimTZtW0efbXKKnRjOoaxD1uTVvQAWxBTx47UEGuQQxa3cWsw9k87zf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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fd5e0e90610>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(S[:, :10], lw=1.5)\n",
    "plt.xlabel('time')\n",
    "plt.ylabel('index level')\n",
    "plt.grid(True)\n",
    "# tag: gbm_dt_paths\n",
    "# title: Simulated geometric Brownian motion paths\n",
    "# size: 60"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Square-Root Diffusion"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "collapsed": false,
    "uuid": "b00481e7-074a-4d04-a65d-4ee95f971116"
   },
   "outputs": [],
   "source": [
    "x0 = 0.05\n",
    "kappa = 3.0\n",
    "theta = 0.02\n",
    "sigma = 0.1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "collapsed": false,
    "uuid": "e085f53a-d065-424e-b1f4-d41c64464c2a"
   },
   "outputs": [],
   "source": [
    "I = 10000\n",
    "M = 50\n",
    "dt = T / M\n",
    "def srd_euler():\n",
    "    xh = np.zeros((M + 1, I))\n",
    "    x1 = np.zeros_like(xh)\n",
    "    xh[0] = x0\n",
    "    x1[0] = x0\n",
    "    for t in range(1, M + 1):\n",
    "        xh[t] = (xh[t - 1]\n",
    "              + kappa * (theta - np.maximum(xh[t - 1], 0)) * dt\n",
    "              + sigma * np.sqrt(np.maximum(xh[t - 1], 0)) * np.sqrt(dt)  \n",
    "              * npr.standard_normal(I))\n",
    "    x1 = np.maximum(xh, 0)\n",
    "    return x1\n",
    "x1 = srd_euler()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "collapsed": false,
    "uuid": "93283652-414e-4773-99ca-00e0b24cc088"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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aO7tgmzUF1q1bP/k13XJzO6e9gaRxWmdRe0qPsD995ZcP18wA88DuiJitMNbl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\nZ05uFgAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fd5e0e52850>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.hist(x1[-1], bins=50)\n",
    "plt.xlabel('value')\n",
    "plt.ylabel('frequency')\n",
    "plt.grid(True)\n",
    "# tag: srd_hist_Euler\n",
    "# title: Simulated square-root diffusion at maturity (Euler scheme)\n",
    "# size: 60"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "collapsed": false,
    "uuid": "59c2b6b1-7c7d-44bd-8ae3-8ad16dd2eb30"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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lLJYvVx/1zz/XTdvjxon4+5caiqdPF2nYUOTsWevrGDJEpFMn6wRX8crwadMs\np1c1FpfbivJLgf4dKcVWQXFVxXqyiI8PdO2KV1AuxRsZAbi4wHffwdmzMG+eytqyJfzT0Z+IjtdT\n4OhA9r4dFqucO3cuKSkp/Pjjj1Z344MPPqBJkybMmDEDgMaNG9OvXz/SNqcxqv0o5m6cy/HU49XW\n4dnfE6/hXpz++LS+n3YdIKL2le7cGe65p27qvOsuOHlSrZmIjYX//U8FEmze3Po6HnkEoqOptOGW\nJZYuhbQ0uPtu2/rp4gKTJsGff0JBgW1lda5BbJEql9uBNTMKEZFZsyS/racYDMjJk2+XS3ruOfVG\nuWmTOk9PF3H6aLsc7NhB4gb1sFid2WyWfv36yfXXX2/VWoioqCjRNE1eeumlctdffPFFcXR0lIj4\nCPF4y0Nu+u4mMZmrry95XbIYMMiZH89Um0+nZopXVP/4Y93VmZQk4uioDNczZyp7Q2KibXXk5or4\n+IhMmVJzW02aqBlIbdRmxWuObLFt6FwdoKueLPDDDyIg+7a3l7CwCeWScnKUT3m7dipWjojI/MXp\n8vW4cZLs4Vals/nPP/8sgKxdu7bG5h999FFxcXGRsxX0D1u3bhVA1qxZI98GfyssQD7e83G1dZnN\nZtnXbZ8E9QjSAwVeBGaz8n677joVTLIuuflm5f3k5CTyxBO1q+OZZ1T56oTM9OkqT4W1oVaTl1e1\nt5TO1Y0uKCwRGysCcvSPobJjh7eYK7y179ql3BcfeUQFdsvPF3nigQdEQM5HVTZoi4gUFBRImzZt\nZNSoUdU2nZSUJK6urjLTwrcxNzdXXF1dZc6cOWI2m2XizxPF9Q1XOZJ0pNo6E79LFAMGSd5Q6hqj\n619LsWYs1q1TT/8339R9+wsXqrpdXETia3Zos0hUlKrj9dctp2/ZotJr8qmoaSzuv1/NXqwJaHil\no39HSrFVUFz9NgqA9u2hRQu8wswYjWlkZx8ulzx4MMyZA4sXQ8OG0KULHN99HwAvzjbwxx9w5kz5\nKp2dnfn3v//Nli1bCA2tepOjRYsWkZeXx9y5cyulubq6MmzYMDZv3oymaXw58UtcHF14Z+c71d5O\n8/ub49LKhfj3460cAJ2yiMBrr6ld4B56qO7rnzwZnJzgn/+EojWbNtOpE4weDV9+CaYKW5nk5Sk7\nxnXXwUsvXVxfp0xRMa22bbu4enSucmyRKpfbgbUzChGRKVMkp3/rIjvFG5WSCwqUH/yLL6q4PTf2\nTBUjDvLtEYi+AAAgAElEQVQKrwiIdO5cucqUlBTx8PAQDw8PeeaZZyS+wutjbm6uNGvWTMaPH19l\nt959910BJLFIx3DTdzfJTd9VXuxXkVPvnVLhxw/o4cdtZdMm9Ta+pGZHs1oTFqbUmhdDsUdWRRfW\nl1+Wcna1iyEnR63xmD374uvSUQRnZMhRGzwi6wN01VMVfPyxmEHC9o2SwEBnSUvbVWORqBbu8mf/\nwdLu9hQByy6O4eHhMnXqVHF0dBQnJyeZNm2aHDp0SEREvv76awFky5aqY0EdPHhQAPmpKLbU/Svu\nl/aftK+xb4VphbLdY7tE3FtLBfU1itmsjL9+fpf/YrOCApGWLVUcqGIOH1ZrNR54oO7aueceEV/f\n6gMa6lhHttEoTXfulB5Bl7cN0VZBUaXqSdO0z6s5PrsEk526ZehQNKDLqftp0KAtkZFTyM8/U22R\nnO7+BMSGc2rYKQD27aucp3v37vz888/ExMTw2GOPsXz5cnr27Mm4ceN455136NOnT0ksJ0v07t0b\nHx8fNm/eDICfpx8JmQmYpXr3VycvJ1rNbkXS70nknsgtF+foWqe6sQgMhF274LnnoEGDS9alWuHs\nDA8/DOvXK5dbs1mFJHd3h48+sq4Oa56LKVMgKQl2WPYGv2q4FN+Rb8+cIbmwkPDsbPZm1LzX/ZVC\ndTaKg8CBouNgmfPi/68sevcGNzecd4bRvfsfGI3pREbejdlctRO556CRtEnJxLf1STRHYe/eqqv3\n9/fn008/JT4+njfeeIPg4GBiYmKYN28emlYx7mEpDg4OjBo1ii1btiAitPFsQ4GpgKTspBpvqfWc\n1miOGqc/Pl1jXh3Fa6+p9TIzZ9Z3T6zj4YdB0+Crr+D779WP+XvvQbNmddfGuHHKNrd8ed3VWYzZ\nbCQ+/iPy8mzbe/5KxGg28+Hp0/R1d8fd0ZEvKxo2r2SsnXoAbrZMVS7FgS2qJxHltxgQICIiZ8/+\nIgYDEhVVtf+icctmEZDbn5sndMiUkSOtbyo3N1d27Nhh1fRz8eLFAsjRo0dl1ZFVwgLkQMIBq9o5\nPP2wbGu0TQqSrwG3lYtk+3albP3kk/ruiW1MnKhUQ40biwwbdvGhRixx551q/426rjs6+mkxGJDo\n6Ll1W/FlyNKzZwWDQVYlJcnso0el4bZtknqZupNR115PmqYN1jTtMCqyK5qm9dY07f/sKLvsx9Ch\nEBoKmZk0b34fbdrMJSHhC86etbzC2jGgLwA9Y7ZDz3SCgqSSB0pVuLq6MnTo0GpnE8WMHj0agM2b\nN9PGU7nJnM6wbpbgN88Pc46ZhP9LsK5j1zBvv61WSP/rX/XdE9t45BGlGsrKUp55DnbwVZwyRUUp\n2L277uo8c+YbTp/+GE1zITX177qr+DJERHgvLo4ujRoxsUkTZrVqRa7ZzP/OnavvrtUJ1jxyn6C2\nM00GEJFQVKC+K48hQ5Sit8jY0KHDu3h7jyQqajaZmcGV83t7k9HGl56xsdAlg+xsjcPlPWvJKsiq\n0Z5QEx06dMDf37+coIjPsM711b27Oz7jfVjz4RpM2VZKsascS7ro8+dh40alymnU6NL36WIYOxaG\nDYM33oCuXW0ra61efsIEZbOpK/VTWtp2oqIepXHjsfj7v0J2dniNNkF7Y08bxabUVMKys5nv54eD\nphHg4UFfd3e+PHOmWPtxRWPVu4mIVFQwGu3QF/szcKBycP/rLwAcHJzo2vVXnJ19iYi4k4KCyvtS\nO/cbQEBcGnRVhqkf1h7jg90fcN/y++j4WUc83vbghc0vXFS3NE1j9OjRGAwGGjdojIuji9UzCoB2\nL7XDlG4i/iN9XUVVrFql3hHqKqbTpcTREbZvh2eftV8bnp5KIK1YocbpYsjNPUFk5F24unaga9dl\n+PiofeSv5lnFu3FxtHZx4YEyQb1mt2pFeHY2+64Co7Y1giJO07QhAJqmuWiaNg84Yt9u2QlPT7j9\ndvjpJygsBMDFxZdu3VZQUHCWyMg7SUz8mvPnl5OS8jcZGftx7H0916WY8PaIB7csPvx9B/P/ns/e\n03vp3aI3g9oMYuH+haTmpl5U10aPHk16ejohwSG09mht9YwCwGuQF6PvGE38e/EUnNcjvBXv8FWW\n339Xi9h69Lj0/alPLI1FVUyZAqdPQ1BQ5TSTCVauhGeegS++gL//hvj4ykLFaMwgPHwiIiZ69FiD\ns7M37u69cHb2JSVl08XdzEViy1jYwv6MDAxpaTzt54dLGb3gfc2a4e7oyJKrwKhtzVaojwKfAq2B\nBGAT8Lg9O2VXZs5UT/zatWoJLeDp2Z/rr1/CsWMPk55e3kewcUPoBfwc8zh3XHeQlln3sn/eJHzd\nfAE4dO4QvRb3YtGBRbw47MVad+vmm28GYMuWLfi18rNpRgHQ/u32JK9J5tTrp+j0eada9+NqJDlZ\nRWJ97jnlQaRjmYkTlUvu8uVq8g2QmgrffKOEw6lTakJuLKNPaNRIRd+94QYYOtTEoEEPkJNzlJ49\n/6JRI/UcapoDjRvfQmrq34iY0bSrKyDEu3FxeDk68q+WLctd93By4v5mzfjp3Dk+vu46vJ2d66mH\nF4+1qqf7RaSZiPiKyAMicsHeHbMbY8dC69bw9dflLrdoMZ2hQ9MYODCOfv3C6d17B927r6Hl+C8A\n6BB7gVG9VhMX404Dk29JuZ7NezL2urF8tu8z8ox5te6Wr68vvXv3LrFT2Coo9p/dT8uZLUlcnEhO\nTE6t+3E1UFEXvWqVeiOeMqV++lOf2KKX9/aGW25RguLIEXjsMRWCZP588PdX71e5uZCYCFu3wqJF\nMGuWcjfeuxcOHXqRjIy17Nv3GdHRoymrmvfxGUNh4Xmysg7V+T1aiz1sFFE5OaxMTuax1q3xdKr8\n3j27yKi99Pz5Om/7UmKNoNitadomTdNmaprW2O49sjeOjjBjhrJTnD5dIckNV1c/3N274+09lKZN\nb6NZ98ehdWuyjvRhZI9ViGgEBZWfb88fPJ9z2edYemjpRXVt1KhR7Nq1i+YNm3M647TNRnL/Bf5o\nLhon/nPiovpR14io/RXqi99/V3GReveuvz5cKUyZomYOXbvCt9/CvfeqvTUCA0tjWLVsCSNHKm+s\njz9WCwL37PmJqVPfIzr6Ud544zEGDoQ+fZQwyciAxo1vASA1tX7VT3XNh/HxuGgac6oI6lVs1F6S\nmHhFG7VrFBQi0gn4L9AdOKhp2lpN0+wQSu0S8s9/KuXq999blz8ggLYn09ndpTsAGzZsLJd8c/ub\n6d2iNx/s+eCiPKBGjx5NQUEB+efzKTAVkJxT2bheFSNGjKBBywb4zfUj6bckMvZfPga0b75R6olN\nl+g3oqwu+sIF2LJFbexzLaqdbNXL33mnUkG9/rqyQXz7bc0C1mTKITZ2Ll5eQ5k581MSE0vdeB97\nDFq1gr17W+Hm1r1eDdp1baM4m5/PD2fPMqNFC5q7uFSZb9ZVYNS2VvW0T0SeBgYAqcAPdu2VvenQ\nAW6+WX0LrHHxCAigaVwsmxxH07x1Inv2GElIWFiSrGka8wfP52jyUdZFrat1t4YNG4azszNH9ilf\nAVvVTwB+8/1wburM8WeP2+UNJi8+j+yj2Vbnz8wsjXD6TvVBce3Cn39eu2qn2uDlBatXq8/M17fm\n/ABnznxLYWEy7du/hYODMx4eKtTIwYPKMN6woRIcjRuPIS1tBybT1aEa/TQhgUIR5vn5VZtvapFR\n+0peqW3NgjsvTdNmaJq2AdgDnAH6271n9mbmTDhxQs2payIgAM1spufxE+Q1c+fo0WFERT1JcvKa\nkix3d72btl5t+WDPB7XukpubG7NmzcLwp9oD8/iF6rdGLUux/tXJ04l2L7cjLTCN6J9SCApSxty6\nIDM4kwN9DnAw4CBp29KsKvPee3DuHEydqgzK+/fXTV+qo6wu+vffVZT5gAD7t3s5Yu/4RmazkdOn\nP8TTcxBeXkPLpWka9O+v1mj89Rd4ed2CSH4lh5FLRV2ORYbRyKKEBO7y9aVjDQtzio3ay86fJ63I\n2/JKw5oZRSjQG3gN6Cwiz4rIlRfrqSJ33gmNG1cyaluk6FdmYPgJcttmkZrqTXr6bRw+fB8ZGQcA\ncHZ05qkbn2L7qe0EJVjwLyxDZuZBLlz4y2La559/zrxZahPvF95+gZSUlBq7d+qU8kq56y7lrTLk\nnVYk4MrO6ccZdKPUydqB9D3phN4ciqO7I67+rhyacIj03enVljl9Gj78EO67T71RennB++9ffF+s\nJTUVNm++dtVOl4KkpN/JyztJ27bPVRmFYMIEta/3kSM3oWku9e4mezGICBtTUpgYHk66ycSzNcwm\niplVhVFbRDicnc27cXE8HROD8WIXsdiLmmJ8AA5FfxvZEhvkUhzYGuupIk88oTY1TkmpPp/ZLNK0\nqfw26g7hpQgBke+/T5Xdu9vJzp3NJD19v5jNZsnIyxCvt71kym+WNztOTw+SsLAJYjAgBoMmmZlh\nFvOZzCZxXOAoDmMcpHPnzhIdbXmXvWKefFLEwUGkSxeRW24RmTFD5LPJ58SAQV4ekChOTmov8NqS\nsjVFtrltk72d9kpuXK7kJebJ3k57ZbvndkkPqrri6dPVLm/Hj6vz559X/azhduqM775TsZ2Cgi5N\ne9caZrNZgoJ6yb59XSrtGlmWtDS1Zetzz4mEhIySoKDul7CXdUOeySTfJCZKt337BINBWu7aJZ/b\nuH1h3/37pUdQkOSbTLI5JUXmREVJhz17BIOh5DDU9FtUR2CHHe4GFsV6OgZXeKynisycCfn5sLQG\nbyVNg4AAAk5FwcALuLoKwcHe9Oy5AZFCgoP7ExTUheTE95nfbworj6wgNiW2pHhGRhCHDk0gOHgA\nGRl78Pd/FScnb2Jj51tszkFzoK13W0ZNHsWFCxcYOHAgO3furLJ7BoMyuRw+rAzG330HTyz3xaOf\nByNPnMTBaLJKw2aJC39dIHx8OK7+rvTe3htXP1catGxAr629cG7izKExh8gMzaxULiQEfvxR7RzY\nvr26NmeO8pqxNkT2xfL772oXu379Lk171xqpqZvIzg7Dz29+tWsjvLxUmLV165SbbHZ2BPn5iZew\np7XnQmEhb5w8Sbs9e5h57BiOmsYPN9zAyYEDecLG7QuLjdpNdu1idFgYixMTuaFRIxZ16sSR/v1x\n1jTWWaFBqBdqkiRAENAWCClzLdIWaWSvg4udUYiI9O0r0quXmjVUx/PPi9HJWVw2bhT/ziYZMEBd\nzs8/L6dPL5KQkJFiMDiIwYB8vw5ZuKm/JCevlbCw8WIwIDt2+MjJk29JYaHakS4u7kMxGJALFzZa\nbG7Yt8Nk+HfDJTo6Wjp37iwuLi7yv//9r1K+8+fVW/PDDxsqpaVsTREDBpnhfFIef9ymUVF1rzwv\ngc6Bsj9gv+Qn5VdKzzmRI7v9dsuOJjskMzyz5LrZLDJypEiTJiKpqeXL/OtfIq6uIufO2d4fazEY\nDJKaqjb4eeYZ+7WzaZPae/tyxp77RIeEjJRdu1qLyVT52ajI+++r5zQqKkQMBuTMmR/s1q+qsHUs\nTuTkiNf27YLBILeGhcnfFy5c1GZEmYWFMiY0VGYeOSKrkpIkq8JOUaNDQ6XLvn21rt8WsMee2XK1\nxHqyxMyZEBYGwRaCApYlIABHYyHdTp7EwTefkBC1d7GLiy+tWz9C795bGTQogU6dFtLApQU3OO0n\nPPw2MjL20b792wwceJJ27V7AyckDgNatH8fVtT2xsfMRqRzMr41nG+Iz4unYsSN79uxh8ODBPPjg\ngyUbHBVTPFPo06dylxuPbEzTO5vyUOEJ0pbbFsXy3M/niLw7Eo9+HvTa0guXppXd/xr6N6TX1l44\nNHAgbHQYOceUN8u6dWqW88orahEXKSnwwguQmckzz6hJ3BdfgLnQTH5CPoVpdW/gW71aRWm5++46\nrxpQLr9jxypX0lWr7NPG5UxGxn7S0gz4+T2Ng0PVrqHFTJig/m7e3BNn52ZXhJ1i2fnzpJtMBAUE\nsKFnT0b7+FgVDboq3J2c2NirF1/fcAOTmjbFzdGxXPptTZpwJCeH47m5F9v1uqcmSQIsB4YAIYAL\nMA9YZos0stdBXcwoUlPVK+6jj1afLzpaBGTmvHniOylJQGTPHstZI85FiM9byOeGqSUzCEsU74mR\nmPhdpbRnNz0rLq+7lLzB5OXliZeXl/zjH/8ol+/RR0Xc3dW2mZYwZhtlTccQ2YxBwr+o+TXebDbL\nqfdPiUEzSMiIECnMLKyxTNaRLNnZbKfsarVLjr91Sub4npSnmpyQmP8cl9j/xErM0B8lmsckstvP\nEnJziCz32Cd/ajvEgEEMGGS3324xFdbtRggTJ6rtTu2xG+XHH6u347FjRW68UZm5tm+v+3YuZ8LD\n75IdO7yrfb7LYjaLtG+vtnWNjHxAdu5sVq1d43Kg34EDMuCAdfvC1AXR2dmCwSCf2Wj7qA3YYUbx\nKCq2U3Gspz5cybGeKuLtrV47ly6FnGr8uzt0AE9P+h2NJbWNcg2tase7bs26MbDdeF7bv5lCqTqc\nVrNm9+Lh0Z8TJ16q5FtestNdjtrprkGDBowfP561a9diKrMpxtatcNNNKkaPJRwbOdJhWXci8SLp\nycMk/VH1znnGDCORd0dyfP5xfO/ypcf6Hji51xwOzO0GN3pt6QVmOPXice5IOsGkCyeJf/MUce/E\ncXpXC84wgYzDYM7IwzegEQZpxtlb/Wn9ZGvy4/NJM1jnbmsN6ekqpPiUKXXr7SSidsh7+mlV9+rV\nKmSYv7+KNRkRUXdtXc7k5ESRnLySVq0eK5kh14SmqVnF1q3g7l7/4TxqIi4vjwOZmdxl7WKSOqBj\no0Z0btiQdRcuwwhJtkiVy+2gLmYUIiKBgeoV8ccfq883fLgE39BD+CRYWrUSuffeqrNuitkkLED+\nOPJHtVWmpm4TgwE5efKNctf/OPKHsAA5mHiw5NqyZcsEkB07doiISEKC6vb771evfzWbRTq1LpRf\nfA5KoHOgJK1JqpQnKyJL9nbeKwZHg8R9GFcrXWzaBZO0aWqUm4eZxFRgUnUUj+1rrymjwcyZIqJ2\namvbViQ33SjbPbbLkX8csbm9qnjxRYOAyO7ddValmM0ic+eqW5kxQ6SwzETr5EmRVq1EWrcWOXWq\n7tqsC+xhozh6dJYEBjaQ/PyzNpXbsEGN37p1iWIwIKdOvVvnfasOW8bi47g4wWCQ6Oxs+3XIAk9H\nR0uDwMBK9ou6hrqaUWia9nk1x2fWCCFN027VNO2opmnRmqY9V0Wez4rSwzRN61N0zVXTtH2apoVq\nmnZY07S3bReBNnDTTdCxo1I8V0dAAF1PROPYJoP27aueUQDc1O4mGjg2YMep6hcXeXvfRJMmk4iL\ne5eCglIfa0s73Y0bNw5nZ2f+/PNPQNkBQHk8VYemwU23OvGMqSduPd2JvCuSC3+VvrWcW3aOgwMO\nYkw30ntrb/zm+tVKF/vO+w6cTnbk3Y8ccHB2UHV8950K7/7MM/D44+r88GGefRbi4mDFGkeaTm5K\n0sokzPnlfciNxtrtjbBtmwpmd+ONtpe1hMmkgt999BE8+aR6TMrGf2vXTi0oy8pSdovL8YWwrsjP\nP8vZsz/QosUMXFya11ygDCNGqGiz69a1xM2t+2Vtp1iZnExPN7caF9PVNROaNCFfhC2pF7dtQZ1T\nlQQBZgDTLRwzgOk1SSDAEYgB/AFn1MK9LhXyjAfWF/1/I7C3TFqjor9OwF5gqIU26k7Evv22et05\neLDqPD/+KALS9dtvZdSEQgGRM2eqzj7s22HS/8v+NTadnX1UDAZHOXbssZJrZzLPCAuQL/Z9US7v\nmDFjpHPnziKiXs69vUWsefn49Vd1e7s3Fsj+PvslsEGgJK9Llqgno8SAQYKHBkteQl7NFVXBuXPK\n1PPAA2UuZmSINGokMmuWOk9KEvH0FJk4UUwmka5dRXr2FElenywGDHL+j/OSny+yZo3I1Kmq6LRp\ntvUjPV3ZDObMsfEGqtgsOi9P5L771Ni99FL1No9t21TbAweKZGXZ2P4VQmzs82IwOEh2du0Ww0yc\nKOLvLxIdPVcCAxuI0Xhp39it4UxenmgGgyw4ceKSt51vMonH9u0y6+hRu7aDjTMKe6qFBgF/lTl/\nHni+Qp7FwL1lzo8CzSvkaQTsB7paaKPuRi41VaR5c5GAgPJ6hbJERIiAPPDiixJwd4aAyKpVVVf5\n4uYXxfFVR8nMz6w6UxHHjj0qBoOjZGerB8RkNonza87y/N/Pl8u3cOFCAeTIkSPSoYPIpEnW3V5y\nsoimibz6qkhBcoEE9QgqMSZHPx0tpoKLMyy+8op6mo6U1SB9/bVUsvq/9Za6tn27fP+9+nf9apMY\nvHbK9x0ixMdHXfPxERk+XP2/dKn1/fjhB1Vm504bOn/smEjjxuV8XbOyRD75RKRNG1Xfu1ZqSVau\nVIsKJ0yo2sHgSqWwMF22b/eSiIi7a13H4sVqPIOD/ypyD/+rDntYNyxOSBAMBjmUWfP31h7cGR4u\nbXbvvihX3Jq4nATFFOCrMucPAp9XyLMGGFzmfDPQV0pnJKFAJvBeFW3U7ej99psakg8+sJxeWCim\nhg3lwylTpPmMBHFyUquNq2JD9AZhAfJ37N81Np2ff1a2b3eX8PA7Sq75f+IvD658sFy++Ph4AeS5\n594REPn0U3XdGv1r//4iQ4YUtXc+XyLujZBzv138goacHJGmTUVuu61CwpAhIjfcUP41PDtbKfMH\nDpT8PLO0bq1+WJ/imGxgm0y7u1DWrhXJz1fyevBgES8vZQeoieho9Xvfvr2hqglCZcxmkTFj1Oc+\nZ46kpIi8/rq6HxC56Sa1XsIWin8Miz+b+qSubBR5eQkSFnarGAxIRkbtPYHi4oq/YtkSGNhAoqPn\n2lxHdna0GI25NpezdizGhIZKp7177fpDXR3fJCYKBoOE2lFQ2SoorNnhrrZYG7q0ojK8WAKYgN6a\npnkBGzVNGyEigRULz5gxA39/fwC8vb3p3bt3STjh4iBgVp83bQqDBjHi5ZfhzjsJPHWqfPrOnYi/\nP32jYjg/LIeO7QP56y94+23L9ZmOm9BOauw4tYPRHUZX276LS3MSEu7h4MFvadNmB97ew3BPdCf8\nTDiojfhK8vft25fly/8EbsTdHcC6+7v++kB+/hnS00fg5etC0iNJJJFEM5rVbryKzqOiRpCcDKNG\nBRIYWJR+7BiBu3bBrFmMKLJ3lJR/7TWYOZPd77zGv/41nIiIEQzt1oyjr65nUudkJky4syT/44/D\nI4+MYNo0ePnlQBwdLfcnPR1uvjmQRgUF/Gd0JvknctkXv6/m/m/bxohNmzjr7MfTS93488tAcnNH\nMGECjB0bSI8eto/H7Nkj+OAD+P33QHr2tL18XZ6HhoZeVHkRoUuXeGJi5nDwYA6tWs3Bw6PvRfWv\nZ88RrFnTCC+vbhw5spKOHT+0qvymTb+RmLgEf/+ttGr1GImJd9vUfmhoaI35M41Gtjo780ybNmzb\ntq1W93ex5+MHDQLgs7VreahFizqpPzAwkO+LtlUo/r20CVukipS+ybtYkWcg5VVPLwDPVcizGLiv\nzHkl1VPR9f8C8yxcr2M5K+qVx91dvWVaeqN49FFJb+Qm2lshcs89Im5u1dsI+izuIyO/H2lV00Zj\ntuza1VLCwsaLiMjU5VPluk+vq5Tv1VdfFdDEx+es9W/OUuqA9Ef1jlg2YTKJXH+90tiVG67nnxdx\ndBRJTKxcyGgU6dZNpFOnEv2M2WSW3W12y6HbDlXKXqyieucdy30wGkVuvVXFEzL0Cy1Rqe3ttFei\nnoyS5A3JYsyx8CFlZUlhG395v+WH0tApXxwwyn33miQ0tBYDUYEHHxRp0cI+6zguFXl5iXLo0EQx\nGJCDB4dIdnZUndT7wgvq0Th27D0xGJCIiHslJWVzlesqjMZsOXFigWzb1lC2bXOVffu6ybZtjaSg\noHxcpPTCQvkwLk7Sq1IdW8EPZ84IBoMEXUxwtDqg34EDMqg6e+lFQl2vo9A0bZumae3LnA8ADlgh\ngw4AnTRN89c0zQW4F1hdIc9qYFpRvQOBNBE5p2laU03TvIuuNwRuQS34sz9+fvD22ypokqUYUAEB\neOZk075hDC0czpOdDZHvr6+yumFth7H39F4KTTWvPnZ0bETz5g+QmrqJwsLUki1R1edayu23TwKE\n9u3X4FDjJ1jKoEHg5la3GwitXw/HjimnphJHKaNRBXoaN05th1YRR0e1OUV0NHz1FQCag4bvvb6k\nbEyhMKX8WE2bptYt/Pe/lhfQP/us8jr67okUOJBK2xfa0vHzjjTs1JAzX54hfFw4u3x2cWj8IdJ2\nlq7XODTnGwad/o35Z+ZyS49zHON6fvnvEXr1uvhxGTgQzp5Vm/9caYgI584tZf/+bqSm/s11131E\nnz7bSvbAvlgmTFCeZKGhj9O69RxSUzcRFjaaffs6cerUW+TnnynTj2UEBd3AyZMLaNJkIgMGHKVL\nl/9hNudw9ux35ep9Jy6OZ2JjmX70KGaxVqFRnhVJSfg1aEA/D+vWh9iLCT4+7M3IILmgoF77UUJN\nkgQYi3rTfxx4C/WDHWCNFALGoYIJxgAvFF2bDcwuk+eLovSw4nqBHkAwykZxCJhfRf32EbdGo3Jd\nadpUeeqU5eBBEZApL78se90HCojM9/la4uMsvzr+Hvm7sADZG7/XqqbT0/cXrdb+Rj7b+5mwADmf\ndb5cnqgos0A76d691Chgrf71tttErqs8Sak1I0Yog285w+26dWoKsGJF1QXNZmWtbtZMeUeJSMaB\nDDFgkIQvEyplv3BBrVW44QZl5iim2F7+7yfMsr/vftnddrds3ri5JN2YY5TkDcq7a1eLXbLbb7fk\nZJnkv48liRMF4uuaLr/+KmKOPCxFYYEvckQUBw6o6n79tU6qqzW22ihMpgIJD7+zaBYxqMS5oi4x\nGjXZRgcAACAASURBVJWzQrFHm9GYK2fPLpWQkBFFkZUd5dCh2+XgwSFiMCD79/eR1NRt5eoIDh4m\ne/a0F7NZzRRTCwrEc/t2ab1rl2AwyJsWjFo1jUVmYaE0CAyUOVF1M3O6GILS0wWDQX6qzq3yIsAe\nxmxgJCq+0xmghS0N2POwm6AQEQkPVwvEHnqo/PXcXDE5Ospb998vq3vcKh29VTgPUD9kd9yhHHs2\nb1bhlc9mnhUWIO/vet+qZs1ms+zZ00FCQ8fKysMrhQVIcGJwuTxLlojAk9KggatkFflhWvuD8Nln\nqq8xMVZlr5biH8P3K97alClKyObXECxu3z5VwSuviIi6972d9krIyBCL2f/+W2V/rMiLePt29RHd\ncotI4lIVVv3MD2eqHIuk1UnyBQelc2vl2vyQ8y+SfLjImG80KpXjv/9t3c3XQEGBchd++uk6qa7W\n2CookpL+FIMBiY59qeRH+GIxmU2VDMP33y/i61vZKzk7O0piYp6VnTubyc6dvpKQ8JXFfpw795sY\nDEhS0moREXn9xAnBYJCQjAy5LzJSNINBNiQnlytT01j8eu6cYDDItoqRLOsBk9kszXfulPsiI0Uy\nM5Wfdh1S54ICZR+IQLm7zi6aIdxmSyP2OuwqKESU4zyIbCyK8JqVJXLPPZLj4iIb+vcX3ztOSl5C\nsux1HCyfjVwpDz4o0rmzlAgOZ2eRkBCRTp91ktt/ud3qZpWvuqPsOqFWd/959M9y6ffdJ+Ljs0UA\nWblypU23dPSo6tuiRTYVs8jUqSIeHkoglpCUpG78qaesq+See0QaNhSJjRURkeMvHxeDZqhyTUfx\n6uiuXdUaks6dRS6cM8me6/ZIUI8gMRurNgosWGAWDbO0cMqR9YwV+fzz8hmGDRMZNKjcpegL0bL2\n2Frr7qUCQ4Yor60riW37x8nqTUjbD1vJ4v2LpcBYex/fnIIcWWBYIA3faCi9F/eWJQeWlLiKL12q\nPse9VUy0zWZjtbGgTKYC2b27jYSGjpbMwkJpsmOHTAhT+7tkGY3SMyhIGu/YIbE5OVb3996ICGm2\nc6cYLxPD0oxdu8T7r7+k0M1NzbzrMKCYPQTFJ0DDMuftgL9tacReh90FRW6ustS2by9y6JBIjx4i\nDg5i7N9fznl7CzNi5exZUYsZWrQoWX+RkiKyfr1y+/zvf0X+ueqf4vOuj5isDIKWkREsBgMSEv2e\nsABZGLSwJM1sVss97ruvQLy9vWX69Ok23ZLZrEJnTJ5sU7FKnDqlDJKV3pg//VQ9VmGWN2WqRHy8\nkjajR4uYzZJ1JEsMGCTu4ziL2XNzlXctqPYPHxb5f/bOOzyKqv3796Yn9F4VpIM0QQERUPBRUbFh\nQbEgIGIDG6I0XXonKl0EKYrSq0jNbBLSCQmhJJTQQyAkkN53Pu8fZ3eTTTYheTTq772e73XNlezM\nmXNmzsyc+5y7fO+ri6+iiUbi74kOzwHQNHXOc13S+F38SG7xQvF4mU8/BU9P9Nxc9p/bz9O/PI3B\naECMQsjV8tM/f/65CsC708Lq3wKzOZe9h9yYtMGFHj/2QIxCs++ase7YOvLN5Vtd7D69m2bfNUOM\nwrO/PkvHpR0Ro1BlRhU+2P0B/qejbN+HI6TnpJOdV/os+uLF6WiasPjcQUTTCCw0YzmXmUl1f386\nhoaWiQ4jKz+fyn9DoNsdkZMDv/4KvXqxqU8fRNPw++orNSNycVG+138BKkr15CkirctT8d+xVbig\nABVuK6Ki1WrUUKuLRYtAhEafHuTAAWDzZvuVhwU9e8L998NPET8hRuHEjRNlalLXdYKDWxJ+tF+x\noLuTJ1VTP/4Ir7/+OrVq1SIvL69cKoZ33lEB0n/COYTPP1cDdTFVcOfOygWqPFiyRN3UTz8BENY5\njCPdSvbV79tXPQ4RmDcrn8N1D3P04aM29UbRvsjIgBYtlG0mdZQRf9nO8YdNxepNW7eSJfcLbeer\nAa7u3LpMPDQRr+leDN8xvHz3BGzapK7xn8ywV5734lL8FjRNmPpHf3RdZ9fpXXRa2gkxCu0Wt2PL\nqS13jC24cPsCz/36HGIU2ixqw8FYZS/SdZ3Ay4G8ufVN3Ke6K6Hx8UM0fvF7pvtN571d7/HUL0/R\nYUkHqs+qjhiFjks7kmcu+SXNyUnAZHJnvO8L9I0orq78IzERg6bx2smT6Lpeal/svHkT0TT2JSWV\nrbP+aqSnKxVs/frqpWnWjGRvb1w0jS/PnVMBwf37q2PvvfenZx8VsaJ41qJuumj5fZ+I7CxPIxW1\n/S2CAuCLL9Sob1GPEBgIIjwzai4LFqCmudWqFbNnTJumejg4+gJiFJaGlV3fc/78RDTNiSbed9kF\n3VlkFLGxsHHjRkQEX1/fcg0I1rjCgIAyn2KHlBQlaIqRIkZEqIoXLXJ4Xokwm5Xap0YNuH6dS7Mv\noYlG5rniaoPsbOWS/P77KvrZ09XMrxJEclDBbLJoX3zxhbosn9WXwNWV2I7foRkK6jfrZib5TKLa\n9CqIUeg6owlrI9faZrTDdwzHa7oXKdnlc5m8ckW1+/33Bfui09MZGh3N1b9Y51wSyvNebPLryZ6D\nQkRcgT7IrJvZcGIDrRe2RoxCq4WteP635xm1ZxRzA+by2/HfCLgcwMXbF5nqOxWPaR5Uml6J2Ydn\nk5PveDBLzEhkXsA8ahlbIEZBjEKt2bXovKwzz6x/hg92f8AHuz9AjMIPR34o9Zq3h7/CHs2Dgzcv\nODw+7eJFRNPwvny51L54Ozqa6v7+5JTH3/yvxLvvqpflqaeUOsJyHX0jIrjXmswoP1/lkxVR30sJ\n2b/S8/NZHR/P0OhoVsTFcc3Bu1YRguKoiFQX+wx3J8rTSEVtf5ugKIr0dMwGA1+/9TZvDbW8WO+8\no0awQiQ/R49icaTRaTCvAYO3DC5zE2lpUWia0G1pcx5Z/Yht/8CBSnWk65CSkoKrqyvvjHmHWf6z\nyMorW7RqUpKakVtsyOXG/PklzJRHj1ZJsv+bWVlMjDr35ZfJupSFJhoXpxVdrhQYtHfvhrPhOXhK\nHg/VTS0xXiEsTKkA3xmuK6t3tWpkH7uKydXEmdHKu8Xvoh9iFJ75ZQABrb3QP7DPTRJyNaTcgt6K\nhg0L+K8y8vNtOZdbBwdzvRyzwuNpadyuQE4QszmPHQec+W5nTYfH88x5/BTxE/1/7k+7xe2oMqOK\nbZAvvL288WUuJztWGxZF/HUzNZtdpNP9GcUmyLqu03NlT+rPq096jmPirDyzmYcDVqNpwuXL8x3f\nl67z/PHjOJeSj/rSlUU84ruAN0+dKtN1/+U4ckR9kA48H+ZbWGwvZhX6ttevV54Sd92lBhlUf4Wl\npDAyJoYqlqx8lS1/RdPoGhaG8cIFjqSmYtb1ChEUIZa/hQVFVHkaqajtHxMUwO2WLdnesyftHrf4\nalpVVIXSleq6WkkOGgSvbHqFuxbcVeb6dV0nJKQtT6yoYwu6M5uVW+HbbxeUe+KJJ6j6elXEKPRa\n1YukzLIN0t26FbPblgl5eUpQ9e5d5EBGhrq4V14pf6VWWJdg27cT/lA4IfcWtwt88onS+2dkwJnR\nZxhlOFO0223IzVWkgw0awO2fd9tN70+9dQrfSr7k3s7l832f4zbVjdTsVOXva81za4Gu63Ra2onO\nyzqXm9Zh4MACd+SRMTGIpjHt4kW8fH3pEBpK4h0Gf13XmXPpEgZNo2NoKMl/Rl9YCvxiFqFpwm/B\nI8t8TnJWMlHXo/j9zO8sC1uG6YKp3O1u364ey4QJxY8FXA5AjMJU36kOz11rCY47ENKNoKBmJXpp\npeTl0To4GCdN48HwcKZeuEC4ZcDMy0vGR3Nhj+bBziu+Ds+vUOi6+hDr1i3iFaIQY0lmtPjqVbv9\n5rAwMps1I75hQxZ+9RWdNmxANA3P/ft5a8UK/MaNQx83jqikJGZcvMiD4eEYLEKjQUBAhQiKVSLy\nuogcF5GWIrJQRJaVp5GK2v5JQZHwyitcrlMH14dvKl2/2axG0P797coNHaq8c74NWIQYhYu3i8+S\nS8L5898w6EfBfao7uq7bNDtrCqUbXrx4MfKZ0OD9BrhNdaP1wtacv3X+jnVPnKhm2uXxBNT1griF\nYmSIVp2Y75/42Kwje8OGXJ17Fk000qLs+W5atVJdnBmbicnVxMl3YujRQ+XnTrCEm1hVDNOnq0va\ntiEHmjVT0eCWgTY1QsVsXJx9kebfNefJn59UJ1st0EUG8MWhixGjEBYXVq5bmjNHXcPKU0oHPtbi\nl3zw1i3cTSa6hIWVuFLIys/nzVOnEE2jyu7lOGmH6BsRQXY51CNlVT0t/KMN+w8JKZkV47dfGoYO\nVe+io/whAzcMpPKMytxIt1ezmHWdtiEhdAgNJd6SKfLmzV0ltnE1O5u31q/ngSNHbLPs+gEBfB3x\nHZom/KF5EBjUvFi0d4XDwkjNqlUOD+u6TvOgILx8fal9+DBV/PxwNZls92BbMaxdy9L33iO5Y0dF\nz1uvHkUDeRJyclgTH89LJ05UiKCoZAm0O2LZpouIR3kaqajtnxQUmZYRoPbzRwsYU8ePV2/89YKE\nLlZ7wE87ziBGYd2xdWVuIz39FB+tE1vQ3YL5OiKKZcSKvZF7EaPQZ1gffC/6Un1WderNrXfHAc3P\nT13XK68oJ4siExYbdF2pmMaOVTNjETXe2o1VubnQpImaGf1Z18LQUHByIuet0WjOGkFNg4h6Loqz\nn5zFb9I1FbcxLpsTg07g6+lLdly2LeTlDYspR9M0oqPVeP/yyxQw1h48aNdURL8Ifm7/M2IUloVZ\nvEl+/VWVLWIcTc5Kxmu6FyN2jijX7Vj7udKsEzxw5IidDvz3xERcTSYeDA8ntchK4Vp2Nj3CwxFN\n4+WQXcr4u3Igomm8evIk5jL2c1kERWJGIr/9IfxyoEl5bu0vQ0qKGttatChOzx5zMwbnyc58+PuH\ndvs3JyQgmsav169jNucSENCQyMjHS23H2hfXLQPmqydPMsH0NDu1ynx8dA0mkyvHjj35l8WP3BGp\nqUrl8MADJdLcA+y4eZOh0dG8f/o0n5w9y1exsXxz/jwzL17E+/JljqY6SEebn6+W0iW4N1aI19O/\ndfsnBQU+PiDCY6+sKBDaVpekb7+1Fbt9W3kHfTXOTLWZ1Xh357tlbyM/n7Vz6jHpEeFm59ZkOTvz\nUnP7aOcppinIN0KX3srT6FTCKZp4N8Fruhe7Tpc8w8rLU7b3ypWxxX00a6bUWitXqjH100/VIklE\neeY9/jj88INy/7XDzz+rQjt2OGyr3LAES1z9RCNqQBQh94bg6+XLKLGomSQYTTRix8XaTpk0SV3C\n3r3qm+vVy2Ibj7imbEcOPpjE3YkM7z0cMQpxqZZocEtudFasKFZ+2PZhVJpeSamoyoiUNDPirOP2\n5iWHPv1bExJw1jQePnqUDIsb55HUVBoFBODl68umGzfotqKbzSYwKHgboml8fva/ywfhCMsCPkXT\nhJDoyX9ZneWFr69S07/3XvFj7+9+H5cpLpxJVDYlXde5LyyMlsHBtpiHCxemomlCenoJmRKNRuWR\nVygfta6bORxQH7/IgSTl5hIXtwxNE2JjHejBKgJjx1JqMMmfxccfq9mSA5XWXyYoRFGAW7edRX+X\np5GK2v5RQXH7Nojw5XMfMWZMof1dukDXrnZFe/eG++6Dp355iraL2pZe740bapB66SWlsxLBLMKR\nRkK+QfB+qJ1d8e4rutPA2AgR4ZgldiE+LZ4uy7vgNNmpYKZcAvLylMF3wQIVVV6rVoHgcHdXiWZW\nr3YgHKzQdRVf0q5dqbOiciE9XcWutGypOMxRg8Pjfc20uDuf6+uvc+W7K+SnF8z8rCEvTZqo3BE2\nb9s33lA3EhtbrBndrNPuo3bc+/G9BbYHXVcebA5GrOArwYhRWH5keZlvZeL580jLVNr3KdnLaf31\n6xg0jccjI1kXH4+nry93BwYSkZpq09MvCllEq4Wt6P5jD0afOYNoGgsul81oXBp0XefLjbU46CPk\n5pYch1IhyM+3GWMBxoxRz61QWhBAsRtUml6Jlza+BMCexERE01hZiHAyJ+cGJpMbp0/brzwAFQPl\n7Kwqb9HCtnxOTQ1H04T4eKXL1XWdmJh30DQhIaEU+hlLe2lpxQksy4yYGLUMHjr0v6/jTggOLvQh\n2OOvFBSPWLbvRGSDiDxjcZX9VUS+LU8jFbX9o4ICSLjrLjb27kuNmjo26nhvb9WthTworMnzxm1T\n3E03M4rnrAaUTqluXRBBb9iQmGd68tmbntT6QnhgalNOVarB1jZC4GWlzL2RfgOD0UDtVW8j7pXo\nXcg+kpaTxtO/PI0YhZn+M8t8T2azWhjt3q1UAneEldfpL+JIssHq3tS/Pxw/TkaGGu9LC/i2qnlE\nNB57DPQA5cbM+PEOy8elxiFG4Z1e73Dbr5Cxpl8/FQBTBLqu03FpR7osL1uciM+tWxg0jdav3qJK\nldJZhn+y5CAQTeOh8HBuWNyAXtzwIjVm1SA9J51vg75FjEJo3BGlZ7aoXkrDnVRPvhd8WfO7sMe/\nXanlKgRWI5LFTzsrC9q3V9qYohRrRs2IGNW7/1B4OHcFBhZzZT116i18fSuRl1doBq3rKqlIzZpo\nM2aoJXTLlhAXZ1mFGMjJKbB/mM3ZHDnSHT+/yqSnnyx2yRkZZ4iJGYnJ5I7J5Ep29n9h09F19V5X\nrWqnpv7LoetqwvXEE8UOVYSNIrws+/6J7Z8WFGeffpqzDRsitbKZb/XOi49XdopCbhzHjlkExVxl\np9gW7YDnOytL6SqrVOHYlqV0WnwfYhRcRvbEySgM8G7Ipd4vcamGMz1X9kTXdVaGr1ZuiQ/4I66/\nI+LF4UKp3fLMeby08SVcp7hyNumvU1XYoU8f5aZXEeHHCxaoqG2Dgd29VaKmOyURGjUKKlXSOH/O\nrAb7hg2hhAQwS8OWIkZhbYu1HH/+eMGBsWOVq66De1oUopwSjsSVnrznZk4ODQMCaB0czPJV+Yio\nBImlYV18PF/FxtqM1edvncdpspMt4PJ21m28pnsxbPswsvLz6X30KG4mEz4lLvfuLCg+2j4ATRPO\nX/Iu/eL+aqSmYktnWEgtGBmpJtovvWRv7krLSaPe3Hp0WzmY/8ydyyoHXPDXE33RNOHq1SUFO61q\n0R9+UH1x+LASFq1aER7UlSNHuhWrJzv7KocP1yM4uKVN6KSkhHL8+ItomgGTyZ2TJ18r1S23VOzc\nqa5p/n9xbnlh5XRPsCcWrQhBES0izQv9biYi0eVppKK2f1xQTJgAIvR64yINGqixHlASvGlTmypG\n1xXtxMAX83Gf6s5ne4tk9dJ1GDYMRJj/eT/EKBg+b4S0X8/jT+jUm1mdx5YKuVNVsE21zzwZPj4C\n9yEvIZ83wLNOrppJVxnIQ7162blwXku9RqXplRi4YeBf3wGWwEO8K3CQSUqC8eP5wGU5lSSN7Nfe\nhlLYPXXdQka7apW6tnUlOw/0/7k/Lb5vQezEWDSDRkaMxdXZmmDcQT6A21m38ZzmWaqtSdd1nomK\nws1k4mhqKqdPq+p+/LHMdw3AJ398gssUF66mFHgavLvzXTymeZCUmcSt3FzuDQmhqp8fx/6LbGiJ\nGYkMXe2Mj4+Qne0gb0hFwupgMGCAMk6cPm07ZF2Br1mD+oZCQ2HaNOI6tyDXokLSa9WCLVsw62Z8\nzvvw9va3qTyjEj/sFLSAlqqilBSbsVjPNxd8n/7+5DTwQjskXDg+ptiloevc9vkW00EDEd4GIg51\nQtMEP79qxMaOs60ijhx5gNDQTuW776wsZQxs2/bvyZUbFaU6c/Fiu90VISj6i8hlEfG1bJdE5Iny\nNFJR2z8tKG5aZgbfLdiESCEaFussphCJl5U2o9eKvjzwwwP2FS1dCiIs618P+caAPDqO515K54hl\n0vrgiq509hbOLf4AROjnsRNxykUmVKXKtJdJuG3GyVlHHtiHiLBnzx676qf6TkWMgu/FAtdVXde5\ndm1lyca/suC559SssIJzC+s6NL07n+danAAvLzVDGjJEWUCL6HO2JSTwWmQkKU2bluqFlZKdgttU\nNz7f9znZ8dn4VfUjqHkQWZezlD1DRNH0OsDQ7UOpPKNyiUbtHRY6iHkWG4KuK8P6O++U/Z6Ts5Kp\nMqMKr2953W7/sevHEKMwL0Cl672clUWjgAAaBQRwOat86UEXBC5gxS7BP7hzuc7700hLU8awp55S\nqhd3dzubUH4+DOlyjPXyKmkeBUazxA4dmD54MEM/fpjMTu1AhI0PeFHlK8Uh9fb2t3nhB0NButZP\nPwWDgZzDoTz5pKLDtxLKXjdNRNOElCeaFKh/UlOVm3c7VffVwV5omhC4zY3Ll+aRl2f/vK9cWYim\nCWlp5ch0ZVW3lTe/7p/Bvfcq745CqCiuJw8R6SwinUTEvTwNVOT2TwsKPT4eRAh44glGtd5H57uT\nlJt+errytHm3YNa5ZYvq7Te9V+A82dnGoklAAGZXFw60dsNtfBVc2u4u5k/+6uZXaTCjEvd4nQMR\n5reYgkybpAgDI38DoG1bH9zbJ+PRuDGdOnXCXEh/m5GbQeMFjbn/h/ttxITXr69H0wSTyY0LF4yY\nzQXG1j1n9tDnpz42LxOHsHp4ff31n+vEMsDa1PLlqI/6s88U46yI4qoePhx27+ZEUhJevr6Itzf9\n5s8nuxSSpQ0nNiBGwf+SPwDJQclKWNwTRNaFTDWyj3DsCht0JahEeolcs5nWwcG0Cg4mt9Az6N9f\n2fxLw5QpipEXYH7g/BJVXL1W9aL5d81tz/JYWhpV/fxoHxpaLCajJNWTruv0Wt7sv1ef/BnMmqWe\nnZWaYsQIFWlciJIiv2s3MtyqsUbeZHStn9m/IZ5mQUHc438AMRpwmSRMeVg5eKQ3rE3WIcWz1uvH\nzuw/5MTpoFfA2RnziHd5+WXVnJOTZuvfkycHc1irge7loSYfnTsXuADefz/89BN6RgZpK77C7CIO\n44Nycm5iMrlw9uznju8zLU2tupcuVYLwwQeVXu355//S7rwjpk6lqF99RQmKnpaguyGiMtK9VZ5G\nKmr7pwUFQEyvXrYZDyKk1m2mghPuu0+9eDt2wMGDpOwNxMXZzOsvhtPqI8EncjvExZFRqypnawot\nvmqO1I52SJM0Zt8YnL92x8U1i5zadTn64ovIjy8jRiebWuK11zScXHRkzDeICOvXr7erY23kWlsc\nR15eGgEBjQgLu8+maw0JaUty8mGirkdReUZlxCjc7X03l5IvOb7xIUPUYF3U6lgBmDu32HuuZn8b\nN6qRtWpV0jw8aLtmDXV//533+vZV8QcnTpRIGT14y2DqzKljx4qaEpKCXzU/gpoGkfnQiyWSG+q6\nToclHbj/h+IG7yVXryKaxrYiOmGjUWlYHLm8gy18BBGIjMqjiXcTeq8qGv6u8OvxXxGjsOdMwcrx\n4K1buJhM9I2IsDPyliQofC/68sqPgqYJmZl3DtD8y5CWpnKVFA5MjY5WN27llLl2Tf2eNo3Dh1Wy\nKnle9etv5xP5RvuGeQHzuJZ6TQ3EzZurzh07li93fcKE35zw+8OZvAY1+PStRBV7MxeGDtUQga1b\n8/H3r8mZAy8WUBGLKEkeUoQNIDNTOZg4MAgDREU9R0BAfcyFyQtnzVIGcytzpYjypOvTR3ljlMDR\nVGGwunwXShxTEaqnn0UkUESWWKKyF4rIwvI0UlHbv0FQXMjMpMauXfywbh3z681mb9WX0Js2tRMe\n1u0R8aGjRCqBUt2L2Nb1SHMVBo9/COdKtxk40LGmZMq+7xCj8MQL3iT28OBE87upNPduxCiMOzgO\nUMS1IiCzI6jbpg3Nmzcnt9Ds0qyb6bq8K40XNObE6S/QNCE5WXmbJCb+TmDg3WzbJzSaW4UG8+qz\n+/Ruqs2sRsvvW3I9rYhnxuXLKrBi9Og/3X830m9wMqG4d0lh9O1b+mxcz8pi8MGDOB06xKF+/aBm\nTeZZvII+PH26GO1Gbn4u1WdVZ+j24q6JKWEp+Ff3J7DqHjJd7ipkeLLHwpCFiFEIv1Zgx0jNy6Pu\n4cP0Pnq0WJt796rnc+hQ8bqsAen166tufXZodMlOD0BOfg715tbj6V+etttvpbR4vQwBeYM2DWLp\nTmdCQv9mtZM1VD0oyH7/s88qdVRGhnIPF1H6deBmeh6V9h1Gvj1Knbo6v/1W5DtJS7OR6iW3uQfv\nl5UA3D1mCCIqfTuofu7SBXr1CiBktZDfoKZyQd+yRRFyiSia/KKwroCOFF/dJSQoxt2kpL1qhzUx\nfa9eMHmyojC4cOGfT57+wAN2E5+KMmYbylPp37X9GwQFwAvHj1PL35+fflHeLdu3o2ba33+v0n26\nuIAIN2q04jOZx4KHO9qEx6qxz3B303yaNi2ZTuO5r7YgRmHloV84PdidfBfBdaLQdXlXPKZ5cDn5\nMmlpqpnmw29Qc84cRISlRbIT+V70RYzCsNXOnDplz3SbnpXI/Ysb4jZF+HFPbW7e3E7A5QC8pnvR\nYUkHew6pTz4pgWO8fDgQe4Dac2rjMc2D4zeOOyyTkqLu68svS65nWVwcomlMvXBBKbgtuVLHnDuH\naBpTLlywK38w9iBiFLZHF+UhUUgNT8W/8iEC5VcytzkOhrqddRuPaR50WNKBF357gQHrB9Dshz7I\nt/fReUVPHlr5EIfOF0iFW7fUI58+vXhdVuPt2okp/KdlOu5VkrhnQctSc0BM8pmEwWgg9pZ9fMgM\nC1vqVw7iRqxYFraM2jPUYHrx4rQSy/3lSE9XqsLHHURQW32bFy9WwTtNmtgG1ymW7HXrwpO5//6C\ncXj37iLj765dmOvVRRfh2iMGVsy8n3fftS8TFQXTnh9KTlVBr1e3IG9KXp7yvhIpThyWkqJWBC++\nWOyyzeZs/P1rcPLkYEVt3KaNcmQpnK/33wArk6fFaaAiBMUmEWlYnkr/ru3fIii0W7cQTWP5D6XY\n3gAAIABJREFUlWs0a6aEt90LnJgIixeT0bE7iJBvUDqG9Lo1GDhQDYQlBWfeugWeLRR7abd93/PB\n1x+BCJ1GCnuPz8Z9qjtDtg1B0zQefBBa35+L+PjQrnt3GjRoQEaRF/bRHxrgOVW4mFhAUaHrOkO3\nD1XCKHQaoaEdLQbBcA7EHsBtqhvdVnRTxtvERGV/KZoithww62am+U7DYDTQelFbas2pS/sl7cnM\nLR65bLXtlEQhFZ6aipvJRP9jx2yzaKu6xazrvGXhSloeV5CH+6PfP8JzmicZuSV/zKm7Y/CX7QTW\n2O+Q7hxgsmkyrRa2ov2S9rRf2hnD/LbUXngfj6x+hNpzanPfsvvsVhatW6uJc2GcOaNsuc8+moev\npy9T5TgiMLF9ILcO3iqRhPBqylWcJzszZp+9146u67x3+rSNSK6o6mlHzA6cJjsxYdu9pUcyVwTm\nzaNw3IQddB26d1d+/x4etpS0CTk5VPHz44XjaiKRlwc/zE2mW4PLVJdb3Nc+l3XrChyIzB99iC5C\nvpOQW0XInD/R5vCgaRpoGrmeTiTXdGfvoiIu41lZavnq4lI86m/iRKVKcsAwe/r0+/j6epI3fby6\nvyLOJP8KXL2qrn+yir6vCEFhEpFkEdn/v8hsx9B1nY6hoXQIDWX5D4qP6cABR+Xg4foxbGw1jrye\nPUCEdnKCefNKrnvqVJDK11S8xC+fsNrCUvv5Ky5omjPfHngSg9HAii0rGDcOXFx0au8PpPeaNYgI\ns2bNstWVlLSXtbsFl8lO3DvuXlq3bs2GDRtshtNJPirdWF5eMn5+lTl1SpEnbY/ejvNkZx5Z/QiZ\nX49Tr81xxyuAOyEpM4mnfnkKMQqvb3mdFyJDcdoyGzEKH/3+UbHyw4eryZwjT8LbubncExRE48BA\nbhaKeSg8OOaazTx17BhOmsaWhAR0XeeuBXfx3K/PlX6huk5atS74u/+BX2XlERXSNoTQTqEceeAI\nR3sdJaJfBBemXEA36wyLjsbVZLLRdKw8uhIxCnvP7rVVOWSIUncXDgLv2xeqVdPZdU84AfUDGDlt\nFB6uqTzidhNNNELuDSFuWZxdFLoVL254kZqzaxYTsHlmM89EReGkaUwtxN4YdCUIz2mePPDDA4SF\n9yQk5A4sAX8lMjLUzT/6aMllrAnACn1An549i5OmccpKArV5szI+F1LpZok7SU612NWxHp4ThC/v\na0GPUa7cus9iI+jSBQID0aZPR3d3J72JMPndcdSt68DElpKiynt6qpgLK27eVO06yCiZnByEpgnX\nBrj8OfbkisbDD6sVTwXRjD/iaCtPIxW1/VsEBcBKS2Ttvhu3aNhQDQCOMHKksnGH700gW9zY0XRU\nicwXqek6lWrmY+hxA5nszLM7RpOSfos0N8H3uU5ERj6GpgnD13ryn7WPsm+fElIvrorDxWTi0f79\nqV69OklJSfj7m3j11RrUqeOMPC7IN0LdDnXx6OCB02QnXtzwol2q1jNnRmMyuZCdrWbiPx/7GYPR\nwFNvGMh5pfgSvCwIiwujiXcTXKe4siR0Ccm5uXj4+uJmMmFY8RJiFDt+Kl1XvGYvv1y8Lt2SZ8DF\nZLJLgekI6fn59AgPx91kYsVppX5bddQxW6cdnniCtNaPE/3eMU6+fpITL50g6tkojvU/RkTfCMK6\nhqGJRsALkbjt0/isEP9STn4OjRc0ps9PfWz7LF7QnLfYjleuVL+/7hKH5qxxYs9+2i9wosvzfri5\n6ZxYGE/YfaoN/+r+xH4VS86NAoHoc96nxHtJz8/ngSNHqObnR7bZzJnEM9SeU5vm3zXn3NWf/35v\npwULKOoyXgz5+SrA0tkZsrO5mJWFm8nEsOho9TJMnqzq6NFD2TG8vTFPnsLZgWPZUu99Wg2tq8gT\nP2uDGAUtuA/RxsroVoO1kxM5nZviv104ejQKV1cHybdAGZtbtVL2i6hCNB1WlWsRVaZuNhO82ZOI\n752VIf7fCusLGBlZMV5P/9bt3yQoMvPzqeXvz/PHj9u+CUe0yVb+/YYNYZvna5irVnOozzyVnk6T\nMZcQgd5rYmm84G7e3PomW09tJaCxcLtbR8zmHE6efB1NEz79RdhydCsuLjDi8xxE0/j0jz8QESpV\nqoSI4OoqPPlkd35Y+wM1ZtWg46KOyDjB61MvbqUVRPcmZSax7shsNM1AbKyF/iIjg2VP10OMwkPL\nu7EsbJldIFhpyMnPYWnYUtymunG39922/NPrLMbXvUlJdA8NQuY2p+qsWsqbhYKEeQ6oamwJXcrK\nd5SYm0uzoCAa/TICp8lOJKQn3Pmk8eO59rQBP9/KDj2DdF3n8rzLaKKxqJPGjev2z9E7yBsxCgGX\nA+zuZ/165eVbowZ0a5bFIdE4uyCQ3w958MdBYbfPKUSUS7+u6yQfTubESyfQDBq+nr6c/eQs2XHZ\n6LpOu8Xt6Lq8q0MV1ZYrV5Cff2ZjXCzNvmtG7Tm1OXPzBMHBLQgObo3Z/Dcl887MVJb6kmZPVpjN\nKthIBPz9GXLqFO4mE5dv3VIzdRF46y2HDgbW5FMNv+6uAlaNBrx91LeRcH61smgPHszJ4GcIDGyM\nruu29CebNzu4losXlUdU/fpgVVteuaLcWz8swie1bh0X3lA2n6ysi/9dH/0duHlTCbovv/zrBIWI\nBFj+potIWpEttTyNVNT2bxIUAONjYzFoGieSMqlVSwWdXrwIu3YpI+agQUpPbV01R35nKjYS5us6\nsy9dwu2gL051s2jdPQdd13lo5UP0Xd2X4TuGs6K7G3rVqqDr6LqZ02c/w9tb2HXAia5dL9O9ez49\nw8NpExLChAkTePbZJ5k40ZOAgP/YBpTvgpUnVfVp1ZGqwpeFrMUvbnhRUVvsb4q/f03y8zPUUkiE\n5es+oem3TW0Zzbos78I32jcciTuCWTeTb87nZMJJVkes5sPfP6Tbim62HMn9f+5PYkYB8dzTx45R\nY+w57r9f59XXzdT/xAcxetBu8SPkm8222KTCdDjx2dl8cvYszprGwOPHHQ6QJbmETrt4EZnbnG4/\n9izT89S3biHkJzUAREc7Jm/bn5RE30kah9w0QtqGkHWxYBBLz0mn1uxaDFg/AFD6dS8v5Sw2aBC4\nueqscQ7hyAsB/LK3CnsOCj6agdjYr+jUqTjdVHp0OqfeOoXmrGFyM3H6/dMs37YcMQp9V/dlfuB8\nom9G2/rkjSFDECcnas4diec0T4KvBHPx4gyLl459fveKgq7r7Jo7gmR3UR5BhZCXl2cjsgSUa6oI\nVK7M8WHDMGgaYyIiFMmmwQBz5qCbzXzzzTeEFHFj7f9zf+rMqUNyVjItvm+B5zRP+qzqRVBQUyIi\nlLrr0KH9+PlVISbmXUv7quo6dYoxXCgcP658lseNK9j3zjvKqBRv4XhKTITatcns3/nvdw74b9C/\nPzRp8r8VxT+JK1lZOFsooK0xLoW3pk2VMbNpU7WiSLypK51hjx4ABCYnc78lsUqXaVcQKbCpDdo0\niObfNaf+vPose7crdjoMYPrK95i5WXj99Wk4O+exNnQGrto+ApKTiY4ehsnkSkZGjK18bn4uXx34\niqPXjjJixAhEhAMHDrDr9C7kawPt5/alo7caJON+f0+198UXbNu2jSVLlhARF8FM/5n0XNkTg9GA\nGIV6c+vZYjDEKFSeUZmHf3qYMfvGsPXUVjvVVlJuLs4bA3H1NNO0aSF39q5q4HN9ZC5VqxYMljdz\ncvji3Dk8fX1x1jSGRkeT4iDb2/qo9fSc1JNZ/rOIjI+0EyR7r55AjMKLf0wq0/O8fXoTmiYE762D\npjnZ9R8ood4pNJSmQUHcOJSEXzU/AhoEkBpRECwxxTQFMQrHrqsBsU8ftZIQgXeqXMLvHj/mbqqh\nssuFjuLEiUH4+VVm3rz0AlNQdrZy/1yyBHSdzNhMYt6NweRqwuRi4pf+v9B9Vndbvzf7rhkjNozA\n1c0VEUEaN2BTxCaysq7g6+vF8eN/T8CXruuM3vkhYhSe/PTuYsc/+OADRAR/fxX0yIQJ4OxM4rhx\ndFm+nGqHDpHUooXS1e5SKsnDhw8jIrxmjZwDjsQdQYzCDL8ZQEEwpfNkZ87Gfm2JFTnHzp3zLQmO\nCujwrblMnn22BPLjAQPUqsJqJDtzRgkP68Rq+HA1S4+M5OjRhwkOblXuLIh/K9asAZH/CYp/GoNO\nnKCanx/xyXlMmqTUggEB9kysu3YpzrlGjcD3o41crV2bNwICbGkKf7l2nbZtdTp1KjB8jtk3xjYQ\n7F73NZbIIVuduq7Tb00/2o56BhGYPfsJNml1+D50JJomnDvngNPGgvT0dNq0aUO9+vWoO7o3Xs3D\ncHXVecZ7PKu2CUFrDaTf14l3hg1TA48InTp1ItCiW0tIT2BN5BoGbxnMh79/yOqI1ZxMOFmqe+eK\nuDjkP9dxc9dt8u7WLfjdJxfPSU8gX7vS4skQVqzLY0JsLJX9/DBoGm+cOsWZElwPreyqdebUsfVV\ng3kNeHv72/x2/DfG/q7sIH0CSs7TURgnTgzCf5eBzA9fxNfXi5MnX7U7bg2uszK4ph1PI7BxIH5V\n/Ejar9yJb2XeovKMyry2WQ1s1hQEzStlst/NxCffN0LTBC1imKoj7RiaJoSFzcHFBb74LF/lU7XO\nNt5+26Z6ybqSxZnRZzC5mQhoFEDM3hiWhC7h6V+exvVJi5AY1BExGHht+HBOnBiEr6/H3xJgp+s6\nn+79VD2H2XchRmHOiYJVzMGDB23v0otWt9OOHcnu3Zu2AQF47N3Lrh49lBdUIceJQYMGISI0atTI\nNiAP3DCQajOrkZylbFVm3UyL71soZ4LodWiaE7Gx4zl79nNMJjfy8uwpZ779VnXtTEckyzt2qIPb\nCsW0vPqqsqVYyf0seQauXVupaEFSKii/xF+BlBRwd/+foPinEZicjGgaS0pKGWdBeDi0aKljcNJx\nfeMMbvsOMj42lrS8PLZuVU/m118LylsHQYPRQELCRTWrKUKfERkfiYyvhJNLHh9/fJENh7ugaYL/\n4Xrk5ZXOGX7kSCQGp3GIIYvKVXOpXBlefjmf4CGVWLlSaHJ3TQwGA+PHj2fTpk00btwYEWHEiBEk\nJalBsTzpKLr+dBoRGD+++OzrXHI8rrPqYph9F1W1fYim8cqJEzbPlytXrtCnTx++/PJLTlsC6iab\nJiNG4YXfXiA7L5u41Dh+iviJQZsGUWNWDZvguHuOE9W134tllCuK7Ox4TCZXzs5tCh06EBs7zsLr\nc4zA5GQejYiwUYIXDm7LupJFaIdQTC4mjj19jDMfnWHk9JE4GZ2IPBzJvh35uDmbWSThfPhxdw75\nCEHhT6AXWm1FRT2Hv38Nnn0mh7WeI9TLMH++ilwWUf7XhRLwpIanEtQsCJOLicvzL2M2m2nVqhVt\n72vLkuM7EMvgOnWqcP78N2V/SP8ldF3ns72fKcPyt/25d/MvuMyshSxoz/xLl0hOTubuu++mVatW\njB49GicnJy77+4MIUz/6iKp+fvh+/73iEivklhQXF4eLiwsNGzZERDh37hwnE04iRmHioYl217Aj\nZgdiFB5f+zhRUQMICGhAcHArIiMfc3C9ShXo5FQsCaLSTzVsqHiprIhUQbO4uKjMXpb3Mi8vBV9f\nD06f/uAv68sKwcCB/xMU/zR0Xef+I0doExJSYnSsrutsTkjg7oMhyGPxiEB3zyDizqSj62ocaN7c\nlt4ZgC2nVNBd9xXd1Y527eyc8q16+Xd2vIPcfZhOXTMJuH2bztoC1p4v+vbbIyIC2nbMsExaNzFt\n2o+MGwcGg87Xhla4uQlVaghLfiugb05NTeWzzz7D2dmZ2rVrs2jRepo00Rk16s5BqFczs5HWKVSp\nn1cs9aUV28/sR4wGanzXnh9P2fuljxw5EmdnZ5ydndXscmgj5W676XXyzHnFbBT55nw2Br7E0NUG\n5m0VhmhD2HgHGoWLF6ehaULGjPfByYnca6fR/Kqx/LCiB6l7+DALLl8m00GSibzkPKKHRxPaKRS/\nqn5srrwZ14muDBgwAE00Dshevn5sOHsOuhAU3K7YDDclJRRNEyKeUiuJs68Uyqe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OAAAg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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fd5e0f57050>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(x1[:, :10], lw=1.5)\n",
    "plt.xlabel('time')\n",
    "plt.ylabel('index level')\n",
    "plt.grid(True)\n",
    "# tag: srd_dt_Euler\n",
    "# title: Simulated square-root diffusion paths (Euler scheme)\n",
    "# size: 60"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "collapsed": false,
    "uuid": "b901c93e-a4a9-4f8f-98d9-69754cb586bf"
   },
   "outputs": [],
   "source": [
    "def srd_exact():\n",
    "    x2 = np.zeros((M + 1, I))\n",
    "    x2[0] = x0\n",
    "    for t in range(1, M + 1):\n",
    "        df = 4 * theta * kappa / sigma ** 2\n",
    "        c = (sigma ** 2 * (1 - np.exp(-kappa * dt))) / (4 * kappa)\n",
    "        nc = np.exp(-kappa * dt) / c * x2[t - 1] \n",
    "        x2[t] = c * npr.noncentral_chisquare(df, nc, size=I)\n",
    "    return x2\n",
    "x2 = srd_exact()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "collapsed": false,
    "uuid": "98648791-2251-4313-baef-e65e4f3ea059"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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eCnwC+N3sTKNOBoovIh6PiAnaf6T/QtJkgW0rwnLjk6TXAt+JiH093q+LQb9b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\ng6qic3nI1O8AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fd5e104ca50>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.hist(x2[-1], bins=50)\n",
    "plt.xlabel('value')\n",
    "plt.ylabel('frequency')\n",
    "plt.grid(True)\n",
    "# tag: srd_hist_exact\n",
    "# title: Simulated square-root diffusion at maturity (exact scheme)\n",
    "# size: 60"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "collapsed": false,
    "uuid": "3d998e1a-e225-4de8-b09b-abf8651d30cb"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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LGTJDvw/NuCw2VrH8/Phj1uo8Tnnwy31fcoznGI47NI5Tjk1h/x39CXfQaIYR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rKRp0551zgL2p6cnDD6+bVmQECPcmXBSenr7ddP+hmiomxdWdeulYX8UlI2sbg4m5rmxJMn33H4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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fd5e9c4ba10>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(x2[:, :10], lw=1.5)\n",
    "plt.xlabel('time')\n",
    "plt.ylabel('index level')\n",
    "plt.grid(True)\n",
    "# tag: srd_dt_exact\n",
    "# title: Simulated square-root diffusion paths (exact scheme)\n",
    "# size: 60"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "collapsed": false,
    "uuid": "fc247695-7a20-4452-8c74-96ace26f2ebe"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "     statistic     data set 1     data set 2\n",
      "---------------------------------------------\n",
      "          size      10000.000      10000.000\n",
      "           min          0.003          0.004\n",
      "           max          0.053          0.053\n",
      "          mean          0.020          0.020\n",
      "           std          0.006          0.006\n",
      "          skew          0.537          0.625\n",
      "      kurtosis          0.379          0.714\n"
     ]
    }
   ],
   "source": [
    "print_statistics(x1[-1], x2[-1])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "collapsed": false,
    "uuid": "7f49cc7d-5264-459c-a9b7-d602daed9f2b"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CPU times: user 662 ms, sys: 13 ms, total: 675 ms\n",
      "Wall time: 675 ms\n"
     ]
    }
   ],
   "source": [
    "I = 250000\n",
    "%time x1 = srd_euler()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "collapsed": false,
    "uuid": "ede482c4-ec2c-43e2-8128-0c97b44469bd"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CPU times: user 1.49 s, sys: 3 ms, total: 1.49 s\n",
      "Wall time: 1.49 s\n"
     ]
    }
   ],
   "source": [
    "%time x2 = srd_exact()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {
    "collapsed": false,
    "uuid": "84a26be5-eede-4478-9f67-c6a97f9804f9"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "     statistic     data set 1     data set 2\n",
      "---------------------------------------------\n",
      "          size     250000.000     250000.000\n",
      "           min          0.003          0.004\n",
      "           max          0.063          0.057\n",
      "          mean          0.020          0.020\n",
      "           std          0.006          0.006\n",
      "          skew          0.563          0.587\n",
      "      kurtosis          0.504          0.511\n"
     ]
    }
   ],
   "source": [
    "print_statistics(x1[-1], x2[-1])\n",
    "x1 = 0.0; x2 = 0.0"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Stochastic Volatility"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {
    "collapsed": false,
    "uuid": "786bc4c9-bff7-4a6d-9ae5-1f62c1813518"
   },
   "outputs": [],
   "source": [
    "S0 = 100.\n",
    "r = 0.05\n",
    "v0 = 0.1\n",
    "kappa = 3.0\n",
    "theta = 0.25\n",
    "sigma = 0.1\n",
    "rho = 0.6\n",
    "T = 1.0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {
    "collapsed": false,
    "uuid": "0db5ac22-1065-4fd5-92a8-3ccb0780d34c"
   },
   "outputs": [],
   "source": [
    "corr_mat = np.zeros((2, 2))\n",
    "corr_mat[0, :] = [1.0, rho]\n",
    "corr_mat[1, :] = [rho, 1.0]\n",
    "cho_mat = np.linalg.cholesky(corr_mat)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {
    "collapsed": false,
    "uuid": "41b7d810-38b5-4831-bb66-84a57c97415b"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 1. ,  0. ],\n",
       "       [ 0.6,  0.8]])"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "cho_mat"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {
    "collapsed": false,
    "uuid": "b16ca288-23eb-463b-9b63-4765eea564f9"
   },
   "outputs": [],
   "source": [
    "M = 50\n",
    "I = 10000\n",
    "ran_num = npr.standard_normal((2, M + 1, I))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {
    "collapsed": false,
    "uuid": "e7ae274e-fec0-43f5-a171-0dd5f131e6c2"
   },
   "outputs": [],
   "source": [
    "dt = T / M\n",
    "v = np.zeros_like(ran_num[0])\n",
    "vh = np.zeros_like(v)\n",
    "v[0] = v0\n",
    "vh[0] = v0\n",
    "for t in range(1, M + 1):\n",
    "    ran = np.dot(cho_mat, ran_num[:, t, :])\n",
    "    vh[t] = (vh[t - 1] + kappa * (theta - np.maximum(vh[t - 1], 0)) * dt\n",
    "          + sigma * np.sqrt(np.maximum(vh[t - 1], 0)) * np.sqrt(dt)  \n",
    "          * ran[1])\n",
    "v = np.maximum(vh, 0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {
    "collapsed": false,
    "uuid": "0016d6a1-4c5c-4617-847a-d0d1510c3fb9"
   },
   "outputs": [],
   "source": [
    "S = np.zeros_like(ran_num[0])\n",
    "S[0] = S0\n",
    "for t in range(1, M + 1):\n",
    "    ran = np.dot(cho_mat, ran_num[:, t, :])\n",
    "    S[t] = S[t - 1] * np.exp((r - 0.5 * v[t]) * dt +\n",
    "                    np.sqrt(v[t]) * ran[0] * np.sqrt(dt))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {
    "collapsed": false,
    "uuid": "5db99fd6-5e32-4c1f-8186-fe6ac910b0c8"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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zS47vETYJrsnBNTlmk+aanG5yTU5zOU/jcTmJfsRncszMzBLnX9aOxjU5UyrV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\n7aRu+wAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fd5e978e510>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, (ax1, ax2) = plt.subplots(1, 2, figsize=(9, 5))\n",
    "ax1.hist(S[-1], bins=50)\n",
    "ax1.set_xlabel('index level')\n",
    "ax1.set_ylabel('frequency')\n",
    "ax1.grid(True)\n",
    "ax2.hist(v[-1], bins=50)\n",
    "ax2.set_xlabel('volatility')\n",
    "ax2.grid(True)\n",
    "# tag: sv_hist\n",
    "# title: Simulated stochastic volatility model at maturity\n",
    "# size: 60"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {
    "collapsed": false,
    "uuid": "0b542695-d86d-47d9-8be4-760cd9a7786b"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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m8NrlhQHXD0D8Q/Eo+7UMUyKnwNrr8tgCRkKip8TG3ov6+iRMm5bU36pcFvRaZBlBED7p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eLVYDbAqBphb2WP4JbBCPIMQlDLIHjYezTqXDk54lI6dwYCAxvOd37b5RmNGBIdjYTycvwSFIQT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\nqGmapuVr/wfTdotP9JT+FgAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fd5e107db90>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, (ax1, ax2) = plt.subplots(2, 1, sharex=True, figsize=(7, 6))\n",
    "ax1.plot(S[:, :10], lw=1.5)\n",
    "ax1.set_ylabel('index level')\n",
    "ax1.grid(True)\n",
    "ax2.plot(v[:, :10], lw=1.5)\n",
    "ax2.set_xlabel('time')\n",
    "ax2.set_ylabel('volatility')\n",
    "ax2.grid(True)\n",
    "# tag: sv_paths\n",
    "# title: Simulated stochastic volatility model paths\n",
    "# size: 60"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {
    "collapsed": false,
    "uuid": "398e803e-e0d8-4bc1-9c2a-53ad78cf524d"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "     statistic     data set 1     data set 2\n",
      "---------------------------------------------\n",
      "          size      10000.000      10000.000\n",
      "           min         20.136          0.176\n",
      "           max        520.205          0.319\n",
      "          mean        108.326          0.243\n",
      "           std         52.848          0.020\n",
      "          skew          1.756          0.178\n",
      "      kurtosis          5.536         -0.006\n"
     ]
    }
   ],
   "source": [
    "print_statistics(S[-1], v[-1])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Jump-Diffusion"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {
    "collapsed": false,
    "uuid": "4d34dbf3-196e-4125-a11d-f967982540e2"
   },
   "outputs": [],
   "source": [
    "S0 = 100.\n",
    "r = 0.05\n",
    "sigma = 0.2\n",
    "lamb = 0.75\n",
    "mu = -0.6\n",
    "delta = 0.25\n",
    "T = 1.0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {
    "collapsed": false,
    "uuid": "b22527e8-afc1-4c69-8253-4e8b6a64f0da"
   },
   "outputs": [],
   "source": [
    "M = 50\n",
    "I = 10000\n",
    "dt = T / M\n",
    "rj = lamb * (np.exp(mu + 0.5 * delta ** 2) - 1)\n",
    "S = np.zeros((M + 1, I))\n",
    "S[0] = S0\n",
    "sn1 = npr.standard_normal((M + 1, I))\n",
    "sn2 = npr.standard_normal((M + 1, I))\n",
    "poi = npr.poisson(lamb * dt, (M + 1, I))\n",
    "for t in range(1, M + 1, 1):\n",
    "    S[t] = S[t - 1] * (np.exp((r - rj - 0.5 * sigma ** 2) * dt\n",
    "                       + sigma * np.sqrt(dt) * sn1[t])\n",
    "                       + (np.exp(mu + delta * sn2[t]) - 1)\n",
    "                       * poi[t])\n",
    "    S[t] = np.maximum(S[t], 0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {
    "collapsed": false,
    "uuid": "19508067-6759-4e88-9276-0d21a0be9e8e"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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LPA3Y3nQAVsn2pgOo0famA6jZ9kUuPzknBiZ1eKyklwMXRsQp5fRa4KmIuLhn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\nAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fd5e1287b50>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.hist(S[-1], bins=50)\n",
    "plt.xlabel('value')\n",
    "plt.ylabel('frequency')\n",
    "plt.grid(True)\n",
    "# tag: jd_hist\n",
    "# title: Simulated jump diffusion at maturity\n",
    "# size: 60"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {
    "collapsed": false,
    "uuid": "27046a97-3c3c-4265-bde7-45f9b71dc001"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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O24q9hf3NDaxeDRMmwIABsHBhpXRVfFi5cmUx4eGTqF37ORo1WkpoVjazo6NZ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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fd5e14439d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(S[:, :10], lw=1.5)\n",
    "plt.xlabel('time')\n",
    "plt.ylabel('index level')\n",
    "plt.grid(True)\n",
    "# tag: jd_paths\n",
    "# title: Simulated jump diffusion paths\n",
    "# size: 60"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Variance Reduction"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {
    "collapsed": false,
    "uuid": "293a9f5c-7ae1-4994-b11d-64ba5312559a"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "           Mean  Std. Deviation\n",
      "-------------------------------\n",
      "-0.011870394558  1.008752430725\n",
      "-0.002815667298  1.002729536352\n",
      "-0.003847776704  1.000594044165\n",
      "-0.003058113374  1.001086345326\n",
      "-0.001685126538  1.001630849589\n",
      "-0.001175212007  1.001347684642\n",
      "-0.000803969036  1.000159081432\n",
      "-0.000601970954  0.999506522127\n",
      "-0.000147787693  0.999571756099\n",
      "-0.000313035581  0.999646153704\n",
      "-0.000178447061  0.999677277878\n",
      " 0.000096501709  0.999684346792\n",
      "-0.000135677013  0.999823841902\n",
      "-0.000015726986  0.999906493379\n",
      "-0.000039368519  1.000063091949\n"
     ]
    }
   ],
   "source": [
    "print \"%15s %15s\" % ('Mean', 'Std. Deviation')\n",
    "print 31 * \"-\"\n",
    "for i in range(1, 31, 2):\n",
    "    npr.seed(1000)\n",
    "    sn = npr.standard_normal(i ** 2 * 10000)\n",
    "    print \"%15.12f %15.12f\" % (sn.mean(), sn.std())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {
    "collapsed": false,
    "uuid": "5940d5f7-72ed-4fd2-8a48-d66c2d5e45db"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "8410000"
      ]
     },
     "execution_count": 46,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "i ** 2 * 10000"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {
    "collapsed": false,
    "uuid": "732f2ba4-3133-4508-92a1-10ee47519f36"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(10000,)"
      ]
     },
     "execution_count": 47,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sn = npr.standard_normal(10000 / 2)\n",
    "sn = np.concatenate((sn, -sn))\n",
    "np.shape(sn)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {
    "collapsed": false,
    "uuid": "3f166fbb-ed57-403f-b251-1b5579ec261d"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "           Mean  Std. Deviation\n",
      "-------------------------------\n",
      " 0.000000000000  1.009653753942\n",
      "-0.000000000000  1.000413716783\n",
      " 0.000000000000  1.002925061201\n",
      "-0.000000000000  1.000755212673\n",
      " 0.000000000000  1.001636910076\n",
      "-0.000000000000  1.000726758438\n",
      "-0.000000000000  1.001621265149\n",
      " 0.000000000000  1.001203722778\n",
      "-0.000000000000  1.000556669784\n",
      " 0.000000000000  1.000113464185\n",
      "-0.000000000000  0.999435175324\n",
      " 0.000000000000  0.999356961431\n",
      "-0.000000000000  0.999641436845\n",
      "-0.000000000000  0.999642768905\n",
      "-0.000000000000  0.999638303451\n"
     ]
    }
   ],
   "source": [
    "print \"%15s %15s\" % ('Mean', 'Std. Deviation')\n",
    "print 31 * \"-\"\n",
    "for i in range(1, 31, 2):\n",
    "    npr.seed(1000)\n",
    "    sn = npr.standard_normal(i ** 2 * 10000 / 2)\n",
    "    sn = np.concatenate((sn, -sn))\n",
    "    print \"%15.12f %15.12f\" % (sn.mean(), sn.std())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {
    "collapsed": false,
    "uuid": "de17794f-4dfd-4441-8d0f-bd097ac0da2c"
   },
   "outputs": [],
   "source": [
    "sn = npr.standard_normal(10000)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {
    "collapsed": false,
    "uuid": "0251bf81-b4d8-4828-80be-9ff972204d06"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-0.001165998295162494"
      ]
     },
     "execution_count": 50,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sn.mean()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {
    "collapsed": false,
    "uuid": "a59c5234-0398-4260-9bcb-d63cd6a7c917"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.99125592020460496"
      ]
     },
     "execution_count": 51,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sn.std()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {
    "collapsed": false,
    "uuid": "699ea494-9c78-4ddc-b153-ce291039f77e"
   },
   "outputs": [],
   "source": [
    "sn_new = (sn - sn.mean()) / sn.std()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {
    "collapsed": false,
    "uuid": "e5836915-236c-4c1b-9012-20fb52e50608"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-2.3803181647963357e-17"
      ]
     },
     "execution_count": 53,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sn_new.mean()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {
    "collapsed": false,
    "uuid": "5113ce74-07a2-4b16-b8d0-7ed9495ccb9b"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.99999999999999989"
      ]
     },
     "execution_count": 54,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sn_new.std()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {
    "collapsed": false,
    "uuid": "f566cd19-61d3-4c69-9391-cb1c906d23c3"
   },
   "outputs": [],
   "source": [
    "def gen_sn(M, I, anti_paths=True, mo_match=True):\n",
    "    ''' Function to generate random numbers for simulation.\n",
    "    \n",
    "    Parameters\n",
    "    ==========\n",
    "    M : int\n",
    "        number of time intervals for discretization\n",
    "    I : int\n",
    "        number of paths to be simulated\n",
    "    anti_paths: boolean\n",
    "        use of antithetic variates\n",
    "    mo_math : boolean\n",
    "        use of moment matching\n",
    "    '''\n",
    "    if anti_paths is True:\n",
    "        sn = npr.standard_normal((M + 1, I / 2))\n",
    "        sn = np.concatenate((sn, -sn), axis=1)\n",
    "    else:\n",
    "        sn = npr.standard_normal((M + 1, I))\n",
    "    if mo_match is True:\n",
    "        sn = (sn - sn.mean()) / sn.std()\n",
    "    return sn"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Valuation"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### European Options"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {
    "collapsed": false,
    "uuid": "693f44be-b3dd-4820-9610-a127f0e9b31b"
   },
   "outputs": [],
   "source": [
    "S0 = 100.\n",
    "r = 0.05\n",
    "sigma = 0.25\n",
    "T = 1.0\n",
    "I = 50000\n",
    "def gbm_mcs_stat(K):\n",
    "    ''' Valuation of European call option in Black-Scholes-Merton\n",
    "    by Monte Carlo simulation (of index level at maturity)\n",
    "    \n",
    "    Parameters\n",
    "    ==========\n",
    "    K : float\n",
    "        (positive) strike price of the option\n",
    "    \n",
    "    Returns\n",
    "    =======\n",
    "    C0 : float\n",
    "        estimated present value of European call option\n",
    "    '''\n",
    "    sn = gen_sn(1, I)\n",
    "    # simulate index level at maturity\n",
    "    ST = S0 * np.exp((r - 0.5 * sigma ** 2) * T \n",
    "                 + sigma * np.sqrt(T) * sn[1])\n",
    "    # calculate payoff at maturity\n",
    "    hT = np.maximum(ST - K, 0)\n",
    "    # calculate MCS estimator\n",
    "    C0 = np.exp(-r * T) * 1 / I * np.sum(hT)\n",
    "    return C0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {
    "collapsed": false,
    "uuid": "f325da52-3e45-4e9e-a4a2-067efb1c3bb7"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "10.044221852841922"
      ]
     },
     "execution_count": 57,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "gbm_mcs_stat(K=105.)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {
    "collapsed": false,
    "uuid": "511974d5-5ceb-4b68-bf7f-e01eaa43f7c6"
   },
   "outputs": [],
   "source": [
    "M = 50\n",
    "def gbm_mcs_dyna(K, option='call'):\n",
    "    ''' Valuation of European options in Black-Scholes-Merton\n",
    "    by Monte Carlo simulation (of index level paths)\n",
    "    \n",
    "    Parameters\n",
    "    ==========\n",
    "    K : float\n",
    "        (positive) strike price of the option\n",
    "    option : string\n",
    "        type of the option to be valued ('call', 'put')\n",
    "    \n",
    "    Returns\n",
    "    =======\n",
    "    C0 : float\n",
    "        estimated present value of European call option\n",
    "    '''\n",
    "    dt = T / M\n",
    "    # simulation of index level paths\n",
    "    S = np.zeros((M + 1, I))\n",
    "    S[0] = S0\n",
    "    sn = gen_sn(M, I)\n",
    "    for t in range(1, M + 1):\n",
    "        S[t] = S[t - 1] * np.exp((r - 0.5 * sigma ** 2) * dt \n",
    "                + sigma * np.sqrt(dt) * sn[t])\n",
    "    # case-based calculation of payoff\n",
    "    if option == 'call':\n",
    "        hT = np.maximum(S[-1] - K, 0)\n",
    "    else:\n",
    "        hT = np.maximum(K - S[-1], 0)\n",
    "    # calculation of MCS estimator\n",
    "    C0 = np.exp(-r * T) * 1 / I * np.sum(hT)\n",
    "    return C0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {
    "collapsed": false,
    "uuid": "44ae2961-ec7c-4e69-b6ff-17b8093a894b"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "7.9500085250284336"
      ]
     },
     "execution_count": 59,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "gbm_mcs_dyna(K=110., option='call')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {
    "collapsed": false,
    "uuid": "bedb79ae-4f01-41ea-b16a-22ea9781fc0e"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "12.629934942682004"
      ]
     },
     "execution_count": 60,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "gbm_mcs_dyna(K=110., option='put')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {
    "collapsed": false,
    "uuid": "e9e52ba0-6ccb-46df-a089-49505d6c7919"
   },
   "outputs": [],
   "source": [
    "from bsm_functions import bsm_call_value\n",
    "stat_res = []\n",
    "dyna_res = []\n",
    "anal_res = []\n",
    "k_list = np.arange(80., 120.1, 5.)\n",
    "np.random.seed(200000)\n",
    "for K in k_list:\n",
    "    stat_res.append(gbm_mcs_stat(K))\n",
    "    dyna_res.append(gbm_mcs_dyna(K))\n",
    "    anal_res.append(bsm_call_value(S0, K, T, r, sigma))\n",
    "stat_res = np.array(stat_res)\n",
    "dyna_res = np.array(dyna_res)\n",
    "anal_res = np.array(anal_res)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {
    "collapsed": false,
    "uuid": "3f9f44ec-47de-4891-bf82-2b620c647c9a"
   },
   "outputs": [
    {
     "data": {
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hqKPgqquCq+83bIg5OBEBoins3wQ+D7wJvEEwQc03IminZGVpLCfNlOdoHDVu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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fd5e9766210>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, (ax1, ax2) = plt.subplots(2, 1, sharex=True, figsize=(8, 6))\n",
    "ax1.plot(k_list, anal_res, 'b', label='analytical')\n",
    "ax1.plot(k_list, stat_res, 'ro', label='static')\n",
    "ax1.set_ylabel('European call option value')\n",
    "ax1.grid(True)\n",
    "ax1.legend(loc=0)\n",
    "ax1.set_ylim(ymin=0)\n",
    "wi = 1.0\n",
    "ax2.bar(k_list - wi / 2, (anal_res - stat_res) / anal_res * 100, wi)\n",
    "ax2.set_xlabel('strike')\n",
    "ax2.set_ylabel('difference in %')\n",
    "ax2.set_xlim(left=75, right=125)\n",
    "ax2.grid(True)\n",
    "# tag: opt_val_comp_1\n",
    "# title: Comparsion of static and dynamic Monte Carlo estimator values\n",
    "# size: 60"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {
    "collapsed": false,
    "uuid": "3f9f44ec-47de-4891-bf82-2b620c647c9a"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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ld9lF/fIiSRbbWPFmVgV0Baa4++ch1qPELtIKn39ev19+883rnrA/8MCN++U1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\niMEuSdKEGOySJE2IwS5J0oQY7JIkTchPVsq13d6tTu8AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fd5e9766b50>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, (ax1, ax2) = plt.subplots(2, 1, sharex=True, figsize=(8, 6))\n",
    "ax1.plot(k_list, anal_res, 'b', label='analytical')\n",
    "ax1.plot(k_list, dyna_res, 'ro', label='dynamic')\n",
    "ax1.set_ylabel('European call option value')\n",
    "ax1.grid(True)\n",
    "ax1.legend(loc=0)\n",
    "ax1.set_ylim(ymin=0)\n",
    "wi = 1.0\n",
    "ax2.bar(k_list - wi / 2, (anal_res - dyna_res) / anal_res * 100, wi)\n",
    "ax2.set_xlabel('strike')\n",
    "ax2.set_ylabel('difference in %')\n",
    "ax2.set_xlim(left=75, right=125)\n",
    "ax2.grid(True)\n",
    "# tag: opt_val_comp_2\n",
    "# title: Comparsion of static and dynamic Monte Carlo estimator values\n",
    "# size: 60"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### American Options"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {
    "collapsed": false,
    "uuid": "033296d5-230b-4b35-ae3f-a2a7ed8c8937"
   },
   "outputs": [],
   "source": [
    "def gbm_mcs_amer(K, option='call'):\n",
    "    ''' Valuation of American option in Black-Scholes-Merton\n",
    "    by Monte Carlo simulation by LSM algorithm\n",
    "    \n",
    "    Parameters\n",
    "    ==========\n",
    "    K : float\n",
    "        (positive) strike price of the option\n",
    "    option : string\n",
    "        type of the option to be valued ('call', 'put')\n",
    "    \n",
    "    Returns\n",
    "    =======\n",
    "    C0 : float\n",
    "        estimated present value of European call option\n",
    "    '''\n",
    "    dt = T / M\n",
    "    df = np.exp(-r * dt)\n",
    "    # simulation of index levels\n",
    "    S = np.zeros((M + 1, I))\n",
    "    S[0] = S0\n",
    "    sn = gen_sn(M, I)\n",
    "    for t in range(1, M + 1):\n",
    "        S[t] = S[t - 1] * np.exp((r - 0.5 * sigma ** 2) * dt \n",
    "                + sigma * np.sqrt(dt) * sn[t])\n",
    "    # case based calculation of payoff\n",
    "    if option == 'call':\n",
    "        h = np.maximum(S - K, 0)\n",
    "    else:\n",
    "        h = np.maximum(K - S, 0)\n",
    "    # LSM algorithm\n",
    "    V = np.copy(h)\n",
    "    for t in range(M - 1, 0, -1):\n",
    "        reg = np.polyfit(S[t], V[t + 1] * df, 7)\n",
    "        C = np.polyval(reg, S[t])\n",
    "        V[t] = np.where(C > h[t], V[t + 1] * df, h[t])\n",
    "    # MCS estimator\n",
    "    C0 = df * 1 / I * np.sum(V[1])\n",
    "    return C0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "metadata": {
    "collapsed": false,
    "uuid": "18dba6e2-2a7f-4474-bbee-227f354fcbc3"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "7.7789332794493156"
      ]
     },
     "execution_count": 65,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "gbm_mcs_amer(110., option='call')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "metadata": {
    "collapsed": false,
    "uuid": "a82c68fc-9820-43a7-8302-3ae0f5a47650"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "13.614023206242445"
      ]
     },
     "execution_count": 66,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "gbm_mcs_amer(110., option='put')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "metadata": {
    "collapsed": false,
    "uuid": "2c4a0f35-5a41-416b-aa39-53d78d1cc366"
   },
   "outputs": [],
   "source": [
    "euro_res = []\n",
    "amer_res = []\n",
    "k_list = np.arange(80., 120.1, 5.)\n",
    "for K in k_list:\n",
    "    euro_res.append(gbm_mcs_dyna(K, 'put'))\n",
    "    amer_res.append(gbm_mcs_amer(K, 'put'))\n",
    "euro_res = np.array(euro_res)\n",
    "amer_res = np.array(amer_res)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "metadata": {
    "collapsed": false,
    "uuid": "6304932d-114f-43b1-ae59-4b0ad2de33fc"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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11UkGDCiyeDfb1u8L/b6oja2qqgqgrt5l0pQm8R2BicChqV2zgXHu/n4O7y1n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\noMAHN0e8OOGGtJkAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fd5e967b550>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, (ax1, ax2) = plt.subplots(2, 1, sharex=True, figsize=(8, 6))\n",
    "ax1.plot(k_list, euro_res, 'b', label='European put')\n",
    "ax1.plot(k_list, amer_res, 'ro', label='American put')\n",
    "ax1.set_ylabel('call option value')\n",
    "ax1.grid(True)\n",
    "ax1.legend(loc=0)\n",
    "wi = 1.0\n",
    "ax2.bar(k_list - wi / 2, (amer_res - euro_res) / euro_res * 100, wi)\n",
    "ax2.set_xlabel('strike')\n",
    "ax2.set_ylabel('early exercise premium in %')\n",
    "ax2.set_xlim(left=75, right=125)\n",
    "ax2.grid(True)\n",
    "# tag: opt_euro_amer\n",
    "# title: Comparsion of European and LSM Monte Carlo estimator values\n",
    "# size: 60"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Risk Measures"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Value-at-Risk"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "metadata": {
    "collapsed": false,
    "uuid": "5473289e-2301-40fb-a665-2d33d43ea09a"
   },
   "outputs": [],
   "source": [
    "S0 = 100\n",
    "r = 0.05\n",
    "sigma = 0.25\n",
    "T = 30 / 365.\n",
    "I = 10000\n",
    "ST = S0 * np.exp((r - 0.5 * sigma ** 2) * T \n",
    "             + sigma * np.sqrt(T) * npr.standard_normal(I))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "metadata": {
    "collapsed": false,
    "uuid": "b2eed114-77e7-479b-b20b-d36a0ffbe636"
   },
   "outputs": [],
   "source": [
    "R_gbm = np.sort(ST - S0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "metadata": {
    "collapsed": false,
    "uuid": "b53e5254-96cc-4294-8ef7-76a2cf21cbca"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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SnjzzSyRJj6P9g5d9FM2t6qp6ger73wF30/4lyAeBn+547k20i5kHgBdWHesi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\nZtbl/wO8NYzvUc7TIAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fd5e138e650>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.hist(R_gbm, bins=50)\n",
    "plt.xlabel('absolute return')\n",
    "plt.ylabel('frequency')\n",
    "plt.grid(True)\n",
    "# tag: var_hist_gbm\n",
    "# title: Absolute returns of geometric Brownian motion (30d)\n",
    "# size: 60"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "metadata": {
    "collapsed": false,
    "uuid": "768aa308-d5c2-4f5d-9936-c19c9321996a"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Confidence Level    Value-at-Risk\n",
      "---------------------------------\n",
      "           99.99           26.072\n",
      "           99.90           20.175\n",
      "           99.00           15.753\n",
      "           97.50           13.265\n",
      "           95.00           11.298\n",
      "           90.00            8.942\n"
     ]
    }
   ],
   "source": [
    "percs = [0.01, 0.1, 1., 2.5, 5.0, 10.0]\n",
    "var = scs.scoreatpercentile(R_gbm, percs)\n",
    "print \"%16s %16s\" % ('Confidence Level', 'Value-at-Risk')\n",
    "print 33 * \"-\"\n",
    "for pair in zip(percs, var):\n",
    "    print \"%16.2f %16.3f\" % (100 - pair[0], -pair[1])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "metadata": {
    "collapsed": false,
    "uuid": "b9952498-c4ad-4d5a-8d3c-3bce1d71006d"
   },
   "outputs": [],
   "source": [
    "dt = 30. / 365 / M\n",
    "rj = lamb * (np.exp(mu + 0.5 * delta ** 2) - 1)\n",
    "S = np.zeros((M + 1, I))\n",
    "S[0] = S0\n",
    "sn1 = npr.standard_normal((M + 1, I))\n",
    "sn2 = npr.standard_normal((M + 1, I))\n",
    "poi = npr.poisson(lamb * dt, (M + 1, I))\n",
    "for t in range(1, M + 1, 1):\n",
    "    S[t] = S[t - 1] * (np.exp((r - rj - 0.5 * sigma ** 2) * dt\n",
    "                       + sigma * np.sqrt(dt) * sn1[t])\n",
    "                       + (np.exp(mu + delta * sn2[t]) - 1)\n",
    "                       * poi[t])\n",
    "    S[t] = np.maximum(S[t], 0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 74,
   "metadata": {
    "collapsed": false,
    "uuid": "37cfd26e-2c44-456a-8b8b-56cf10e12aac"
   },
   "outputs": [],
   "source": [
    "R_jd = np.sort(S[-1] - S0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 75,
   "metadata": {
    "collapsed": false,
    "uuid": "3300cad0-872b-45ef-9b12-3fc3507b2c54"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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ZLoo5m4HFTfOjxb85FB8G32SsEP4gsITiL8k6FcK/DlyQpi8CvjbZe6nTA/jv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\nAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fd5e0eee250>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.hist(R_jd, bins=50)\n",
    "plt.xlabel('absolute return')\n",
    "plt.ylabel('frequency')\n",
    "plt.grid(True)\n",
    "# tag: var_hist_jd\n",
    "# title: Absolute returns of jump diffusion (30d)\n",
    "# size: 60"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 76,
   "metadata": {
    "collapsed": false,
    "uuid": "8adcca19-77bf-4d8e-a342-1a5cc1cadd69"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Confidence Level    Value-at-Risk\n",
      "---------------------------------\n",
      "           99.99           75.029\n",
      "           99.90           71.833\n",
      "           99.00           55.901\n",
      "           97.50           45.697\n",
      "           95.00           25.993\n",
      "           90.00            8.773\n"
     ]
    }
   ],
   "source": [
    "percs = [0.01, 0.1, 1., 2.5, 5.0, 10.0]\n",
    "var = scs.scoreatpercentile(R_jd, percs)\n",
    "print \"%16s %16s\" % ('Confidence Level', 'Value-at-Risk')\n",
    "print 33 * \"-\"\n",
    "for pair in zip(percs, var):\n",
    "    print \"%16.2f %16.3f\" % (100 - pair[0], -pair[1])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 77,
   "metadata": {
    "collapsed": false,
    "uuid": "812884b3-c147-4799-8b7a-93eb62a9b1fc"
   },
   "outputs": [],
   "source": [
    "percs = list(np.arange(0.0, 10.1, 0.1))\n",
    "gbm_var = scs.scoreatpercentile(R_gbm, percs)\n",
    "jd_var = scs.scoreatpercentile(R_jd, percs)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 78,
   "metadata": {
    "collapsed": false,
    "uuid": "b960f3cc-fed3-4cfa-9189-040931e4ab09"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(-90.0, 0.0)"
      ]
     },
     "execution_count": 78,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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PArd567cD9wN1NXxbXRK4NoXbbnN3DC1awAUXuMdWN2yAwsKgozPGpKHdJggR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\nQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fd5e9c21890>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(percs, gbm_var, 'b', lw=1.5, label='GBM')\n",
    "plt.plot(percs, jd_var, 'r', lw=1.5, label='JD')\n",
    "plt.legend(loc=4)\n",
    "plt.xlabel('100 - confidence level [%]')\n",
    "plt.ylabel('value-at-risk')\n",
    "plt.grid(True)\n",
    "plt.ylim(ymax=0.0)\n",
    "# tag: var_comp\n",
    "# title: Value-at-risk for geometric Brownian motion and jump diffusion\n",
    "# size: 60"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Credit Value Adjustments"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 79,
   "metadata": {
    "collapsed": false,
    "uuid": "92795f2e-84b4-4881-960f-91a39eb1cc77"
   },
   "outputs": [],
   "source": [
    "S0 = 100.\n",
    "r = 0.05\n",
    "sigma = 0.2\n",
    "T = 1.\n",
    "I = 100000\n",
    "ST = S0 * np.exp((r - 0.5 * sigma ** 2) * T \n",
    "             + sigma * np.sqrt(T) * npr.standard_normal(I))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 80,
   "metadata": {
    "collapsed": false,
    "uuid": "3e3c6a61-c268-44f4-bce9-f3c2f83faac9"
   },
   "outputs": [],
   "source": [
    "L = 0.5"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 81,
   "metadata": {
    "collapsed": false,
    "uuid": "f06f2c7d-8c1a-4cc3-b171-dad76994c6b9"
   },
   "outputs": [],
   "source": [
    "p = 0.01"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 82,
   "metadata": {
    "collapsed": false,
    "uuid": "38b71c82-76a1-4299-992f-93820cbf2677"
   },
   "outputs": [],
   "source": [
    "D = npr.poisson(p * T, I)\n",
    "D = np.where(D > 1, 1, D)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 83,
   "metadata": {
    "collapsed": false,
    "uuid": "46418aea-2253-4f09-840a-1c45676bda2c"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "99.981825216842921"
      ]
     },
     "execution_count": 83,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.exp(-r * T) * 1 / I * np.sum(ST)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 84,
   "metadata": {
    "collapsed": false,
    "uuid": "fe7436d3-4eb4-40f4-9d4c-c5efa0e3d3a0"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.5152011134161355"
      ]
     },
     "execution_count": 84,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "CVaR = np.exp(-r * T) * 1 / I * np.sum(L * D * ST)\n",
    "CVaR"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 85,
   "metadata": {
    "collapsed": false,
    "uuid": "3070c8f6-8a77-4373-b423-f6871170dbaf"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "99.466624103426781"
      ]
     },
     "execution_count": 85,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "S0_CVA = np.exp(-r * T) * 1 / I * np.sum((1 - L * D) * ST)\n",
    "S0_CVA"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 86,
   "metadata": {
    "collapsed": false,
    "uuid": "d7d14139-b76d-4c11-a57b-930db11abd3c"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "99.48479888658386"
      ]
     },
     "execution_count": 86,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "S0_adj = S0 - CVaR\n",
    "S0_adj"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 87,
   "metadata": {
    "collapsed": false,
    "uuid": "c6995617-5021-4d8f-9f94-8fca0571ff89"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1031"
      ]
     },
     "execution_count": 87,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.count_nonzero(L * D * ST)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 88,
   "metadata": {
    "collapsed": false,
    "uuid": "fc6e6717-9ffc-486c-a736-3892c277f3e6"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(0.0, 175)"
      ]
     },
     "execution_count": 88,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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DN/sahQ+ptWoYRo3ifwF/JekW4B/SvoiIP57tRs3MrD661igkfSV9uhL4i3Tdl6ePIwc/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\nfgAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fd5e9c8d910>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.hist(L * D * ST, bins=50)\n",
    "plt.xlabel('loss')\n",
    "plt.ylabel('frequency')\n",
    "plt.grid(True)\n",
    "plt.ylim(ymax=175)\n",
    "# tag: cva_hist_stock\n",
    "# title: Losses due to risk-neutrally expected default (stock)\n",
    "# size: 60"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 89,
   "metadata": {
    "collapsed": false,
    "uuid": "59b7c831-c915-4c06-a23b-0ac913220d76"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "10.427336109660052"
      ]
     },
     "execution_count": 89,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "K = 100.\n",
    "hT = np.maximum(ST - K, 0)\n",
    "C0 = np.exp(-r * T) * 1 / I * np.sum(hT)\n",
    "C0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 90,
   "metadata": {
    "collapsed": false,
    "uuid": "da0198e3-10bc-4324-8e0e-b09c2e61e94d"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.053822578452208093"
      ]
     },
     "execution_count": 90,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "CVaR = np.exp(-r * T) * 1 / I * np.sum(L * D * hT)\n",
    "CVaR"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 91,
   "metadata": {
    "collapsed": false,
    "uuid": "24d26328-f3f2-4da4-8d5c-7fb06a70eec8"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "10.373513531207843"
      ]
     },
     "execution_count": 91,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "C0_CVA = np.exp(-r * T) * 1 / I * np.sum((1 - L * D) * hT)\n",
    "C0_CVA"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 92,
   "metadata": {
    "collapsed": false,
    "uuid": "a221dbb8-eec3-45e1-abd7-146050c0285f"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "582"
      ]
     },
     "execution_count": 92,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.count_nonzero(L * D * hT)  # number of losses"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 93,
   "metadata": {
    "collapsed": false,
    "uuid": "e1becbb6-7a1e-49bb-8a8e-b7daab189c6e"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1031"
      ]
     },
     "execution_count": 93,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.count_nonzero(D)  # number of defaults"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 94,
   "metadata": {
    "collapsed": false,
    "uuid": "44c3d031-8002-4bba-abd7-0db5451b2d52"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "43995"
      ]
     },
     "execution_count": 94,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "I - np.count_nonzero(hT)  # zero payoff"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 95,
   "metadata": {
    "collapsed": false,
    "uuid": "b132d24e-093b-45e6-a4cc-29b8ef006038"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(0.0, 350)"
      ]
     },
     "execution_count": 95,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fd5e114a490>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.hist(L * D * hT, bins=50)\n",
    "plt.xlabel('loss')\n",
    "plt.ylabel('frequency')\n",
    "plt.grid(True)\n",
    "plt.ylim(ymax=350)\n",
    "# tag: cva_hist_opt\n",
    "# title: Losses due to risk-neutrally expected default (call option)\n",
    "# size: 60"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Conclusions"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Further Reading"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<img src=\"http://hilpisch.com/tpq_logo.png\" alt=\"The Python Quants\" width=\"35%\" align=\"right\" border=\"0\"><br>\n",
    "\n",
    "<a href=\"http://www.pythonquants.com\" target=\"_blank\">www.pythonquants.com</a> | <a href=\"http://twitter.com/dyjh\" target=\"_blank\">@dyjh</a>\n",
    "\n",
    "<a href=\"mailto:analytics@pythonquants.com\">analytics@pythonquants.com</a>\n",
    "\n",
    "**Python Quant Platform** |\n",
    "<a href=\"http://oreilly.quant-platform.com\">http://oreilly.quant-platform.com</a>\n",
    "\n",
    "**Derivatives Analytics with Python** |\n",
    "<a href=\"http://www.derivatives-analytics-with-python.com\" target=\"_blank\">Derivatives Analytics @ Wiley Finance</a>\n",
    "\n",
    "**Python for Finance** |\n",
    "<a href=\"http://shop.oreilly.com/product/0636920032441.do\" target=\"_blank\">Python for Finance @ O'Reilly</a>"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 2",
   "language": "python2",
   "name": "python2"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 2
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
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